{"id":55,"date":"2023-09-17T07:27:50","date_gmt":"2023-09-17T07:27:50","guid":{"rendered":"https:\/\/mathority.org\/it\/operazioni-con-monomi-esempi-ed-esercizi-risolti-1-2-3-4-quali\/"},"modified":"2023-09-17T07:27:50","modified_gmt":"2023-09-17T07:27:50","slug":"operazioni-con-monomi-esempi-ed-esercizi-risolti-1-2-3-4-quali","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/operazioni-con-monomi-esempi-ed-esercizi-risolti-1-2-3-4-quali\/","title":{"rendered":"Operazioni con i monomi"},"content":{"rendered":"<p>In questa pagina spieghiamo come eseguire tutte le operazioni con i monomi (addizione, sottrazione, moltiplicazione, divisione e potenza). Inoltre, potrai vedere esempi di ogni tipo di operazione con monomi ed esercitarti con esercizi risolti passo dopo passo.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Suma-y-resta-de-monomios\"><\/span> Addizione e sottrazione di monomi <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Due o pi\u00f9 monomi possono essere sommati o sottratti solo se sono monomi simili, cio\u00e8 se i due monomi hanno una parte letterale identica (stesse lettere e stessi esponenti).<\/p>\n<p> Allora la somma (o sottrazione) di due monomi simili \u00e8 uguale ad un altro monomio composto dalla stessa parte letterale e dalla somma (o sottrazione) dei coefficienti di questi due monomi. <\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-37\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/somme-de-monomes-exemples.png\" alt=\"cosa sono le operazioni con i monomi\" width=\"200\" height=\"201\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/soustraction-de-monomes-1.png\" alt=\"operazioni con monomi 1 che\" class=\"wp-image-151\" width=\"200\" height=\"202\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<p> L&#8217;addizione e la sottrazione di monomi sono anche chiamate rispettivamente addizione e sottrazione di monomi.<\/p>\n<h3 class=\"wp-block-heading\"> Esempi di addizione e sottrazione di monomi<\/h3>\n<p> Affinch\u00e9 tu possa capire chiaramente come sommare e sottrarre due o pi\u00f9 monomi, ti lasciamo diversi esempi di seguito: <\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e5b7ccd3830be06fd2f5165a760b367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x^6+3x^6 = 7x^6\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"125\" style=\"vertical-align: -2px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74bf65eaed8bbd99077260cff7a731dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5y^3-2y^3 = 3y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"122\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bdda97aea0b54fdbbc1ffb190d88fb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x^2y+5x^2y-3x^2y = 4x^2y\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"211\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75b17946f2dc3a4f4f7ec9753107b88d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6abc-7abc+4abc = 3abc\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"202\" style=\"vertical-align: -2px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60b660491e258b4dbcc9728dfd75d7ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^3y^2-4x^3y+2x^2y^3 = \\color{red} \\bm{\\times}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"228\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<p> I monomi dell&#8217;ultimo esempio non possono essere sommati n\u00e9 sottratti perch\u00e9 non sono simili o, in altre parole, hanno incognite o esponenti diversi. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Producto-de-un-numero-por-un-monomio\"><\/span> Prodotto di un numero di volte monomiale <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Per risolvere il <strong>prodotto di un monomio per un numero,<\/strong> moltiplica semplicemente il coefficiente del monomio per quel numero, lasciando invariata la parte letterale del monomio. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-ou-multiplication-d-un-nombre-par-un-monome.png\" alt=\"\" class=\"wp-image-393\" width=\"165\" height=\"167\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> Esempi di moltiplicazione di numeri per monomi <\/h3>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e92d21eb9de394440a08b38dcbc685d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2\\cdot (6x^3) = (2\\cdot 6)x^3 = 12x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"207\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-318cfda7f7d93cc2a20639b21e82fb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-4\\cdot (5x^7) = (-4\\cdot 5)x^7 = -20x^7\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a2dab19c0282d641053ffb115e6bf28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5\\cdot (-3a^4b) = (5\\cdot (-3))a^4b = -15a^4b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"283\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-83efc00f783524ec9b40eac2196931f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-7(-6x^9y^5)= (-7\\cdot (-6))x^9y^5=42x^9y^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"313\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Multiplicacion-de-monomios\"><\/span> Moltiplicazione di monomi <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> Il risultato della <strong>moltiplicazione di due monomi<\/strong> \u00e8 un altro monomio il cui coefficiente \u00e8 il prodotto dei coefficienti dei monomi e la cui parte letterale si ottiene moltiplicando le variabili che hanno la stessa base, cio\u00e8 sommando i loro esponenti. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/multiplication-de-monomes-1.png\" alt=\"operazioni con monomi pdf\" class=\"wp-image-203\" width=\"194\" height=\"196\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Pertanto, per moltiplicare due monomi diversi, dobbiamo moltiplicare i coefficienti tra loro e sommare gli esponenti delle potenze che hanno la stessa base.<\/p>\n<p> Tuttavia, <strong>se moltiplichiamo due monomi con potenze di base diverse<\/strong> , dobbiamo semplicemente moltiplicare insieme i loro coefficienti e lasciare le stesse potenze. Per esempio:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91a6b9c012d06d618d61f97a1648fc3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x^2\\cdot 3y^4 = (5\\cdot 3) x^2y^4 = 15x^2y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> D&#8217;altra parte, quando si moltiplicano i monomi, \u00e8 necessario tenere conto della regola dei segni:<\/p>\n<ul>\n<li> Un monomio positivo moltiplicato per un monomio positivo d\u00e0 un altro monomio positivo.<\/li>\n<li> Un monomio positivo moltiplicato per un monomio negativo (o viceversa) equivale a un monomio negativo.<\/li>\n<li> Due monomi negativi moltiplicati insieme danno origine a un monomio positivo.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> Esempi di moltiplicazioni monomiali<\/h3>\n<p> Di seguito sono riportati alcuni esempi di moltiplicazione tra monomi in modo da poter vedere come \u00e8 fatto: <\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c373ccffc9ccd101ba2ce02e99abf7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^4 \\cdot 7x^5= (6\\cdot 7)x^{4+5} = 42x^9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"228\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ca04a0873a835eb55f0b7c34208302d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4y \\cdot 2y^3 = (4\\cdot 2)y^{1+3} = 8 y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d47775082b2bf643cd6277a4e74b5b08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5x^2y^4\\cdot (-8x^8y^2)=(5\\cdot (-8))x^{2+8}y^{4+2} = -40x^{10}y^6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"390\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2eac10c8abaa8979578beaf8274bd93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x^6y^4 \\cdot (-4x^2z)= (-3\\cdot (-4)) x^{6+2}y^4z= 12x^8y^4z\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"389\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca7602e907500c26d357e713da3bde13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3x^8\\cdot 4x^5\\cdot (-x^2) =-12x^{13}\\cdot (-x^2)= 12x^{15}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"341\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<p> Come hai visto, risolvere una moltiplicazione di monomi \u00e8 relativamente semplice. Ma dovresti tenere presente che i monomi possono anche essere moltiplicati per polinomi, e anche 2 o pi\u00f9 polinomi possono essere moltiplicati insieme. Se sei pi\u00f9 interessato, puoi vedere come funzionano tutte queste operazioni cliccando su <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/moltiplicazione-di-polinomi-esempi-esercizi-prodotti-risolti-moltiplicazione\/\">Moltiplicazione polinomiale<\/a><\/span><\/strong> .<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Division-de-monomios\"><\/span> Divisione dei monomi <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> In matematica, il risultato della <strong>divisione dei monomi<\/strong> \u00e8 un altro monomio il cui coefficiente \u00e8 equivalente al quoziente dei coefficienti dei monomi e la cui parte letterale si ottiene dividendo le variabili che hanno la stessa base, cio\u00e8 sottraendo i loro esponenti . <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/division-de-monomes-1.png\" alt=\"operazioni con monomi 2 che\" class=\"wp-image-317\" width=\"201\" height=\"202\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Ovviamente qualsiasi divisione di monomi pu\u00f2 essere espressa anche come frazione:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d022dbe3ddc38f031f0bb5dd4a8a6b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3y^2z : 2x^2y = \\cfrac{8x^3y^2z}{2x^2y} =  4xyz\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"243\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Come nella moltiplicazione, nella divisione dei monomi \u00e8 necessario applicare la legge dei segni:<\/p>\n<ul>\n<li> Un monomio positivo diviso per un monomio positivo d\u00e0 un altro monomio positivo.<\/li>\n<li> Un monomio positivo diviso per un monomio negativo (o viceversa) equivale a un monomio negativo.<\/li>\n<li> Due monomi negativi divisi tra loro danno origine a un monomio positivo.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> Esempi di divisione di monomi<\/h3>\n<p> Di seguito puoi vedere altri esempi di come vengono divisi due o pi\u00f9 monomi: <\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0345d3bf8afc735b7e499584142fef76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"7x^6 : 7x^4= (7:7)x^{6-4} = 1x^2=x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"264\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ba837b0d16f0fe2c78d057c053a72c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12y^5 : 4y^2= (12:4)y^{5-2} = 3y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"237\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99ce1c658885782a0de61d4acaae8f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"15x^7y^6 :3x^4y^5= (15:3)x^{7-4}y^{6-5} = 5x^3y\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"318\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-344fa60ffc830f331035b6307b698695_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27x^9y^7 :(-3x^5y^2)= (27:(-3))x^{9-5}y^{7-2}= -9x^4y^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"395\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f98903cc9dff2fc60d4baeef41bbce1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-18x^{13} : 3x^4 : (-2x^7) = -6x^9: (-2x^7) = 3x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"348\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<p> Sicuramente ad un certo punto, quando hai imparato qualcosa di nuovo in matematica, ti sei chiesto: <span style=\"text-decoration: underline;\">a cosa serve<\/span> ? Ebbene, la divisione monomiale viene utilizzata per dividere i polinomi. In effetti, \u00e8 abbastanza comune commettere un errore dividendo i polinomi perch\u00e9 due monomi sono stati divisi in modo errato. Per questo motivo ti consigliamo, ora che hai familiarit\u00e0 con la divisione tra monomi, di vedere come si calcola la <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/divisione-di-polinomi-esempi-esercizi-risolti-dividere\/\">divisione tra polinomi<\/a><\/span><\/strong> , perch\u00e9 ora ti sar\u00e0 molto pi\u00f9 semplice imparare la procedura (\u00e8 piuttosto complicata).<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Potencia-de-un-monomio\"><\/span> Potenza di un monomio <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> In matematica, <strong>per calcolare la potenza di un monomio, ogni elemento del monomio viene elevato all&#8217;esponente della potenza<\/strong> . In altre parole, la potenza di un monomio consiste nell&#8217;elevare il suo coefficiente e le sue variabili (lettere) all&#8217;esponente della potenza. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/puissance-dun-monome-exemple.png\" alt=\"come si risolvono le operazioni con i monomi\" class=\"wp-image-362\" width=\"179\" height=\"180\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Ricorda dalle propriet\u00e0 delle potenze che quando entrambi elevano un termine gi\u00e0 elevato, gli esponenti si moltiplicano. Ecco perch\u00e9 <strong>, alla potenza di un monomio, l&#8217;esponente di ciascuna lettera va sempre moltiplicato per l&#8217;esponente che indica la potenza<\/strong> .<\/p>\n<p> D&#8217;altra parte, per effettuare correttamente questa operazione \u00e8 necessario ricordare la seguente propriet\u00e0 dei poteri:<\/p>\n<ul>\n<li> Un monomio negativo elevato ad esponente pari equivale a un monomio positivo.<\/li>\n<li> Invece, un monomio negativo elevato a un esponente dispari risulta in un monomio negativo.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> Esempi di potenze di monomi<\/h3>\n<p> Vi lasciamo con alcuni esempi affinch\u00e9 possiate comprendere chiaramente come si calcola la potenza di un monomio: <\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1e51fcc4fe828722bfa6963d3540e08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(5x^6\\right)^2 = 5^2\\left(x^6\\right)^2 = 5^2x^{6\\cdot 2} = 25x^{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"268\" style=\"vertical-align: -7px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-488af8cc2d389d0a9012531e595a51e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(2x^5\\right)^4 = 2^4\\left(x^5\\right)^4 = 2^4x^{5\\cdot 4} = 16x^{20}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"268\" style=\"vertical-align: -7px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-931e60b61878fcf9dda31deb0eac0178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(-4y^3\\right)^2 = (-4)^2\\left(y^3\\right)^2 = (-4)^2y^{3\\cdot 2} = 16y^{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"326\" style=\"vertical-align: -7px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:25px\"><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43073f3940619cc05ddaf143d91031ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(3x^4y\\right)^3 = 3^3\\left(x^4y\\right)^3 = 3^3x^{4\\cdot 3}y^{1\\cdot 3} = 27x^{12}y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"331\" style=\"vertical-align: -7px;\"><\/p>\n<p><\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-841e3847493c3454e6e0cde2b389de9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(-2a^5b^7\\right)^3 = (-2)^3\\left(a^5b^7\\right)^3 = (-2)^3a^{5\\cdot 3}b^{7\\cdot 3} = -8a^{15}b^{21}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"417\" style=\"vertical-align: -7px;\"><\/p>\n<p><\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Operaciones-combinadas-con-monomios\"><\/span> Operazioni combinate con monomi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Una volta che hai visto quali sono tutte le operazioni con i monomi, sappi che possono anche essere combinate tra loro. Possiamo cio\u00e8 trovare esercizi in cui ci viene chiesto di risolvere operazioni con monomi in cui sono coinvolte tutte le tipologie: addizione, sottrazione, moltiplicazione, divisione e potenze.<\/p>\n<p> Ma non preoccuparti, non sono cos\u00ec difficili come sembrano. L&#8217;unica cosa che devi ricordare \u00e8 l&#8217;ordine in cui vengono risolte le operazioni combinate:<\/p>\n<ol style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">Innanzitutto vengono risolte le operazioni con i monomi tra parentesi.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">Successivamente si calcolano le potenze dei monomi.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">In terzo luogo, vengono eseguite moltiplicazioni e divisioni dei monomi.<\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">Infine, vengono determinate le addizioni e le sottrazioni dei monomi.<\/span><\/li>\n<\/ol>\n<p> Sono sicuro che risolvendo un esempio lo vedrai pi\u00f9 chiaramente:<\/p>\n<h3 class=\"wp-block-heading\"> Esempio di operazione combinata di monomi<\/h3>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ec50305026b5ae600feeedc2063ffb2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^9:(2x^4-8x^4)+3x^4\\cdot 6x - (x^3\\cdot 7x^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Innanzitutto dobbiamo risolvere le operazioni con i monomi tra parentesi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20a79022126a4016bee178da5b2fd9a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^9:(-6x^4)+3x^4\\cdot 6x - 7x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"231\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> In questo caso non abbiamo alcun potere. Quindi ora calcoliamo le moltiplicazioni e le divisioni dei monomi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-75343501bfbe74ef63de85b90ce916c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x^5+18x^5 - 7x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"144\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> E infine, aggiungiamo e sottraiamo i monomi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8dc32e179e406eb902f611c60ad1c0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"16x^5 - 7x^5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5da0d3692c51151ea9c2a0478ffaa720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{9x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-operaciones-con-monomios\"><\/span> Esercizi risolti su operazioni con monomi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nel caso in cui vogliate esercitarvi, vi lasciamo di seguito diversi esercizi risolti passo passo di difficolt\u00e0 ESO su operazioni con monomi.<\/p>\n<h3 class=\"wp-block-heading\"> Esercizio 1<\/h3>\n<p> Calcolare le seguenti addizioni e sottrazioni di monomi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d2245ec403db8426a7c6747356beaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 2x^4+9x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"100\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91d825e366ebde8630a08439cd57befe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -3x^5y^3 +4x^5y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f85bb7e0260af1c6e593b98fe852ad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 3x^8-6x^8+2x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"148\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0254b78b2cce547d32a5eac7675b5a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ -2a^3b^2-5a^3b^2+3a^3b^2-7a^3b^2+4a^3b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"340\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-864766b992d12d73d145c8075df256df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 6xyz-5xz-7xyz-8xz\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c83fa020e8457b4402f2b7da01617f8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 6y^3+2y^3-y^5+8y^4-y^5-5y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"270\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Vedi la soluzione<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56d30d2625c1f94ae6c667438b259524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 2x^4+9x^4= \\bm{11x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4db7d7a7554cb1731e350df37305e936_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ -3x^5y^3 +4x^5y^3= \\bm{x^5y^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"214\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-598471a47e39a79742bf6e01dcbae7c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 3x^8-6x^8+2x^8= \\bm{-x^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"204\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07daa6a36995cfe314093771fa52e921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ -2a^3b^2-5a^3b^2+3a^3b^2-7a^3b^2+4a^3b^2=\\bm{-7a^3b^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"419\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea6b3c423007edf6eee13c5fa69eafc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 6xyz-5xz-7xyz-8xz= \\bm{-xyz-13xz}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"345\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b81f9ed371675cfe8a51f608c3da025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 6y^3+2y^3-y^5+8y^4-y^5-5y^3 = \\bm{-2y^5+8y^4+3y^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"428\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Esercizio 2<\/h3>\n<p> Risolvi le seguenti moltiplicazioni di monomi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-753999a2a1f5487e6842243827fddc38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 5x^7\\cdot 6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da823cb11d28cc8c5150d9c82bede60c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 2y^8\\cdot (-5y^6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-facd1f9e25fe39a2f2ea7099c220faca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -4a^3 \\cdot (-2a)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a48b54dd3a3b028e42698709e3256ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 2x^3\\cdot 4x \\cdot (-3x^6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60d398af3d95ef228ed8404701bba1e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ -5x^6\\cdot (-x^3) \\cdot (-9x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60666db89889355be28e2381482c2146_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 7x^3y^2 \\cdot 5x^8z^4 \\cdot (-2x^2y^5z^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"224\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Vedi la soluzione<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-462ca864ae7df79cca6d598a907ef47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 5x^7\\cdot 6x^2=(5\\cdot 6)x^{7+2} = \\bm{30x^9}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"254\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9df50340278ae741ac52f48a38ee5200_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 2y^8\\cdot (-5y^6)= (2\\cdot (-5))y^{8+6} = \\bm{-10y^{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5b53bea16638f6a6d33c5ec2276a3e3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -4a^3 \\cdot (-2a) =(-4\\cdot (-2))a^{3+1} = \\bm{8a^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"324\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88b62aecb02121fb27d5290456ae05cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 2x^3\\cdot 4x \\cdot (-3x^6) = 8x^4\\cdot (-3x^6) = \\bm{-24x^{10}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"349\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2738eff1187ab32a1f1d526051dce513_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ -5x^6\\cdot (-x^3) \\cdot (-9x^4)=5x^9\\cdot (-9x^4) =\\bm{-45x^{13}}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"396\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 131px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d92004db2f9cc2fc28f7b5358dcb5932_l3.png\" height=\"131\" width=\"865\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\text{F)} \\ 7x^3y^2 \\cdot 5x^8z^4 \\cdot (-2x^2y^5z^3)= <span class=&quot;ql-right-eqno&quot;>   <\/span><span class=&quot;ql-left-eqno&quot;>   <\/span><img src=&quot;https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bb20ebb96e0dff759d07813f6fff9470_l3.png&quot; height=&quot;22&quot; width=&quot;195&quot; class=&quot;ql-img-displayed-equation quicklatex-auto-format&quot; alt=&quot;\\[35x^{11}y^2z^4\\cdot (-2x^2y^5z^3) =\\]&quot; title=&quot;Rendered by QuickLaTeX.com&quot;\/> \\bm{-70x^{13}y^7z^7}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221;><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Esercizio 3<\/h3>\n<p> Determinare il risultato delle seguenti divisioni di monomi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a538bc97a4e40a71e36ea49db97f40fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 24x^4: 6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-457fde039e753413817c083f0cb26ab5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 16a^9: (-2a^6)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"128\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-596179812c3d61c3aa87a965e1265aca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -21x^3:(-3x)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"144\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a9a8fd439d22ab3a8f601ee400b758e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 14x^8y^3 :2x^6y\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61d294ce86a62652f898caad643e4aff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 42x^5y^3z^6 : 7x^2y^3z^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de91d460fe9753ba75b7be2ad58e9599_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{F)} \\ 48x^8y^6z^{10} : (-6x^4y^{2}z^4) : (-4x^2y^2z^3)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"305\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Vedi la soluzione<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78e36b09fd9b819a65269c31c08da492_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 24x^4: 6x^2 = (24:6)x^{4-2} = \\bm{4x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0bcef3f5ee4e08629f22b3cb5fca73d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 16a^9: (-2a^6)= (16:(-2))a^{9-6} = \\bm{-8a^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"332\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d98b9bd4b6894c24bd28b2a4f0ff002_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ -21x^3:(-3x) = (-21:(-3))x^{3-1} = \\bm{7x^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"349\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5896be1f204d342ff20cbbe7bfa587a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ 14x^8y^3 :2x^6y = \\bm{7x^2y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8edc35d562476b2352abcba054635cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 42x^5y^3z^6 : 7x^2y^3z^4= 6x^3y^0z^2=\\bm{6x^3z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"320\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nell&#8217;operazione precedente abbiamo semplificato il termine<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0f4ce4bf65bd54e5fc728271a7d7d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> perch\u00e9 qualsiasi numero elevato a 0 \u00e8 uguale a 1. Quindi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07d692d378ec44f656fcde7667d5aab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^3y^0z^2=6x^3\\cdot 1 \\cdot z^2=\\bm{6x^3z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"228\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 131px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1b1554d59ad6a39e24db564712789ee7_l3.png\" height=\"131\" width=\"618\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"\\text{F)} \\ 48x^8y^6z^{10} : (-6x^4y^{2}z^4) : (-4x^2y^2z^3)=<span class=&quot;ql-right-eqno&quot;>   <\/span><span class=&quot;ql-left-eqno&quot;>   <\/span><img src=&quot;https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6dc0e068dbf84cef6abfe7e1789d245b_l3.png&quot; height=&quot;22&quot; width=&quot;194&quot; class=&quot;ql-img-displayed-equation quicklatex-auto-format&quot; alt=&quot;\\[-8x^4y^4z^6: (-4x^2y^2z^3)=\\]&quot; title=&quot;Rendered by QuickLaTeX.com&quot;\/> \\bm{2x^2y^2z^3}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221;><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Esercizio 4<\/h3>\n<p> Trova le seguenti potenze dei monomi: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3fd531461cb852f7cf8f4e4f6505c96f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(-8x^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"93\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f74d8697d4ba1a59d074b73d2555430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(-2a^7\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"91\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aca4350f00eb97562878ce29f48a96f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(5x^8y^2\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"96\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d9bcc48ef1555d5459cf28aa1abb3c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(-x^3y^5z\\right)^6\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"110\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe946ceee571ae61db828c15b6a47cbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ \\left(-2x^5y^4\\right)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"109\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Vedi la soluzione<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20a7243c8e76a50f25b1da07921e231e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(-8x^4\\right)^2=(-8)^2\\left(x^4\\right)^2 = (-8)^2x^{4\\cdot 2} = \\bm{64x^{8}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"361\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-718c9fcf2f66c2e2e7d874e80dc3a921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(-2a^7\\right)^3=(-2)^3\\left(a^7\\right)^3 = (-2)^3a^{7\\cdot 3} = \\bm{-8a^{21}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"368\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-71162deddf3bccc8fbc9107769152d4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(5x^8y^2\\right)^3=(5)^3\\left(x^8y^2\\right)^3 = \\bm{125x^{24}y^6}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"303\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7eaa22bf4eb0e520c6ecdfa31c1585ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(-x^3y^5z\\right)^6=(-1)^6\\left(x^3y^5z\\right)^6 = \\bm{x^{18}y^{30}z^{6}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"338\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c1f52fd47fc66e0f3178c63a0b864be8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ \\left(-2x^5y^4\\right)^5 =(-2)^5\\left(x^5y^4\\right)^5 = \\bm{-32x^{25}y^{20}}\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"342\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Esercizio 5<\/h3>\n<p> Risolvi le seguenti operazioni combinate con i monomi e semplifica il pi\u00f9 possibile: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c95dec30cc01c49200d9ce7e198edfe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ 3x^2\\cdot 4x^5 : 2x^4 + 10x^6:(-2x^4)\\cdot 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"292\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd210aaafaf98000f5ee202936c30d7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ 4\\cdot \\left(5x^4 -2x^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"145\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-321e95fdde4c962fb0e532486180d6bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ 8x^7:(-4x^3+3x^3-7x^3)-5x^3\\cdot 3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"298\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981ccad0ae5f55e1d6d1db15b8aa2694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\left(-2x^2y\\right)^3+4x^2 \\cdot 5\\left(xy\\right)^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"277\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f33fd1cdef957f1e2818fa88968ea5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{E)} \\ 8x^8:\\left(-2x^3\\right)^2-(7x^3\\cdot 6x^6): (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"301\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Vedi la soluzione<\/strong> <\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5710afdc30e5dade5d481dad0d5cd77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{A}\\bm{)} \\color{black} \\ 3x^2\\cdot 4x^5 : 2x^4 + 10x^6:(-2x^4)\\cdot 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"366\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-485388f25e43e12a37c10f917feeca41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^7 : 2x^4 -5x^2\\cdot 6x\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"156\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ee2fc488bcde1db8ffaa4326ac5b7d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x^3 -30x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"83\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89b11cc611350a670562c01e942c5415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-24x^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01e9be21288169c2354a463f1c40361c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{B}\\bm{)} \\color{black} \\ 4\\cdot \\left(5x^4 -2x^4\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"219\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1cc01826641601698450b1862bf36083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot \\left(3x^4 \\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"72\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c970af842b560696a361e3380b8d3b7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4\\cdot 9x^8\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-87e1df6f571f6df50dbf3e897219a02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{36x^8}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b1c6034fb28968d509dc49474cd65955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{C}\\bm{)} \\color{black} \\ 8x^7:(-4x^3+3x^3-7x^3)-5x^3\\cdot 3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"372\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-61a4c1b0fb98fe84ddcdbe7882098549_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^7:(-8x^3)-5x^3\\cdot 3x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"176\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a281b2cc5f0fb342b44088ce0813682_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x^4-15x^4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9ec10abaebfd5fdc5e42ccc865332f25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-16x^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-83f6044f7e0b53ec6897720463a94fde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{D}\\bm{)} \\color{black} \\ \\left(-2x^2y\\right)^3+4x^2 \\cdot 5\\left(xy\\right)^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"350\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-96d9d1b07bd2838d25894be6ccc8fb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3+4x^2 \\cdot 5\\cdot x^4y^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"234\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d4d6c7bf71a47be8084fd867bdf497ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3+4x^2 \\cdot 5x^4y^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-79f03ec9d21f0dc8873f5bb951838d30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3+20x^6y^4:(-2y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"190\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c12ffd09529b975082bfe1f73098b7d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-8x^6y^3-10x^6y^3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"130\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-63fd4ee3643afe01035c8189415c1e27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{-18x^6y^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-603b9ac5ea94315d1329b4960dcb2f12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\color{blue} \\mathbf{E}\\bm{)} \\color{black} \\ 8x^8:\\left(-2x^3\\right)^2-(7x^3\\cdot 6x^6): (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"374\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0453c3029ccff9ac02828970e9ee9c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^8:\\left(-2x^3\\right)^2-42x^9: (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"231\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6cc9b09bf2b39f9ea04eb1b61587dfbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^8:4x^6-42x^9: (-2x^4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-474309bfcc65106dde914093f76f624c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{2x^2+21x^5}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> L&#8217;operazione non pu\u00f2 essere ulteriormente semplificata perch\u00e9 i due monomi hanno esponenti diversi, quindi il risultato \u00e8 un polinomio.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Se sei arrivato fin qui, significa che hai gi\u00e0 padroneggiato tutte le operazioni con i monomi. Luminoso! Bene, un&#8217;altra operazione che sicuramente ti interesser\u00e0 \u00e8 il fattoriale di un numero. Si tratta di un&#8217;operazione piuttosto curiosa, poich\u00e9 viene calcolata diversamente dalle altre. E, in effetti, molte persone non sanno quale sia il fattoriale di un numero. Scopri come risolvere un <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/it\/funzione-fattoriale-di-un-numero\/\">fattoriale<\/a><\/span><\/strong> cliccando su questo link.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In questa pagina spieghiamo come eseguire tutte le operazioni con i monomi (addizione, sottrazione, moltiplicazione, divisione e potenza). Inoltre, potrai vedere esempi di ogni tipo di operazione con monomi ed esercitarti con esercizi risolti passo dopo passo. Addizione e sottrazione di monomi Due o pi\u00f9 monomi possono essere sommati o sottratti solo se sono monomi &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/operazioni-con-monomi-esempi-ed-esercizi-risolti-1-2-3-4-quali\/\"> <span class=\"screen-reader-text\">Operazioni con i monomi<\/span> Leggi altro &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[17],"tags":[],"class_list":["post-55","post","type-post","status-publish","format-standard","hentry","category-rappresentazione-delle-funzioni"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Operazioni con monomi -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/it\/operazioni-con-monomi-esempi-ed-esercizi-risolti-1-2-3-4-quali\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Operazioni con monomi -\" \/>\n<meta property=\"og:description\" content=\"In questa pagina spieghiamo come eseguire tutte le operazioni con i monomi (addizione, sottrazione, moltiplicazione, divisione e potenza). 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