{"id":10828,"date":"2017-06-05T21:16:04","date_gmt":"2017-06-05T21:16:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10828"},"modified":"2018-01-11T18:59:05","modified_gmt":"2018-01-11T18:59:05","slug":"multiplying-monomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/multiplying-monomials\/","title":{"raw":"Multiplying Monomials","rendered":"Multiplying Monomials"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the power and product properties of exponents to multiply monomials<\/li>\r\n \t<li>Use the\u00a0power and product properties of exponents to simplify monomials<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe now have three properties for multiplying expressions with exponents. Let\u2019s summarize them and then we\u2019ll do some examples that use more than one of the properties.\r\n<div class=\"textbox shaded\">\r\n<h3>Properties of Exponents<\/h3>\r\nIf [latex]a,b[\/latex] are real numbers and [latex]m,n[\/latex] are whole numbers, then\r\n\r\n[latex]\\begin{array}{cccc}\\text{Product Property}\\hfill &amp; &amp; &amp; \\hfill {a}^{m}\\cdot {a}^{n}={a}^{m+n}\\hfill \\\\ \\text{Power Property}\\hfill &amp; &amp; &amp; \\hfill {\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\hfill \\\\ \\text{Product to a Power Property}\\hfill &amp; &amp; &amp; \\hfill {\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\hfill \\end{array}[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168467221786\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property.<\/td>\r\n<td>[latex]{x}^{12}\\cdot {x}^{20}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the exponents.<\/td>\r\n<td>[latex]{x}^{32}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146171[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\left(-7{x}^{3}{y}^{4}\\right)}^{2}[\/latex]\r\n[reveal-answer q=\"412728\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"412728\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469890733\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(-7{x}^{3}{y}^{4}\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take each factor to the second power.<\/td>\r\n<td>[latex]{\\left(-7\\right)}^{2}{\\left({x}^{3}\\right)}^{2}{\\left({y}^{4}\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property.<\/td>\r\n<td>[latex]49{x}^{6}{y}^{8}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146174[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]\r\n[reveal-answer q=\"625558\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"625558\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168465997267\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Raise [latex]6n[\/latex] to the second power.<\/td>\r\n<td>[latex]{6}^{2}{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]36{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Commutative Property.<\/td>\r\n<td>[latex]36\\cdot 4\\cdot {n}^{2}\\cdot {n}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the constants and add the exponents.<\/td>\r\n<td>[latex]144{n}^{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice that in the first monomial, the exponent was outside the parentheses and it applied to both factors inside. In the second monomial, the exponent was inside the parentheses and so it only applied to the <em>n<\/em>.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146177[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\left(3{p}^{2}q\\right)}^{4}{\\left(2p{q}^{2}\\right)}^{3}[\/latex]\r\n[reveal-answer q=\"299315\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"299315\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468310384\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(3{p}^{2}q\\right)}^{4}{\\left(2p{q}^{2}\\right)}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power of a Product Property.<\/td>\r\n<td>[latex]{3}^{4}{\\left({p}^{2}\\right)}^{4}{q}^{4}\\cdot {2}^{3}{p}^{3}{\\left({q}^{2}\\right)}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property.<\/td>\r\n<td>[latex]81{p}^{8}{q}^{4}\\cdot 8{p}^{3}{q}^{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Commutative Property.<\/td>\r\n<td>[latex]81\\cdot 8\\cdot {p}^{8}\\cdot {p}^{3}\\cdot {q}^{4}\\cdot {q}^{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the constants and add the exponents for\r\n\r\neach variable.<\/td>\r\n<td>[latex]648{p}^{11}{q}^{10}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146179[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Multiply Monomials<\/h3>\r\nSince a monomial is an algebraic expression, we can use the properties for simplifying expressions with exponents to multiply the monomials.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(4{x}^{2}\\right)\\left(-5{x}^{3}\\right)[\/latex]\r\n[reveal-answer q=\"762661\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"762661\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469853450\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(4{x}^{2}\\right)\\left(-5{x}^{3}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Commutative Property to rearrange the factors.<\/td>\r\n<td>[latex]4\\cdot \\left(-5\\right)\\cdot {x}^{2}\\cdot {x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-20{x}^{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146195[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(\\Large\\frac{3}{4}\\normalsize{c}^{3}d\\right)\\left(12c{d}^{2}\\right)[\/latex]\r\n[reveal-answer q=\"867589\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"867589\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466307238\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(\\Large\\frac{3}{4}\\normalsize{c}^{3}d\\right)\\left(12c{d}^{2}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Commutative Property to rearrange\r\n\r\nthe factors.<\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\normalsize\\cdot 12\\cdot {c}^{3}\\cdot c\\cdot d\\cdot {d}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]9{c}^{4}{d}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146196[\/ohm_question]\r\n\r\n<\/div>\r\nFor more examples of how to use the power and product rules of exponents to simplify and multiply monomials, watch the following video.\r\n\r\nhttps:\/\/youtu.be\/E_D8PO1G7gU","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the power and product properties of exponents to multiply monomials<\/li>\n<li>Use the\u00a0power and product properties of exponents to simplify monomials<\/li>\n<\/ul>\n<\/div>\n<p>We now have three properties for multiplying expressions with exponents. Let\u2019s summarize them and then we\u2019ll do some examples that use more than one of the properties.<\/p>\n<div class=\"textbox shaded\">\n<h3>Properties of Exponents<\/h3>\n<p>If [latex]a,b[\/latex] are real numbers and [latex]m,n[\/latex] are whole numbers, then<\/p>\n<p>[latex]\\begin{array}{cccc}\\text{Product Property}\\hfill & & & \\hfill {a}^{m}\\cdot {a}^{n}={a}^{m+n}\\hfill \\\\ \\text{Power Property}\\hfill & & & \\hfill {\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\hfill \\\\ \\text{Product to a Power Property}\\hfill & & & \\hfill {\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467221786\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td>[latex]{x}^{12}\\cdot {x}^{20}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the exponents.<\/td>\n<td>[latex]{x}^{32}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146171\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146171&theme=oea&iframe_resize_id=ohm146171&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\left(-7{x}^{3}{y}^{4}\\right)}^{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q412728\">Show Solution<\/span><\/p>\n<div id=\"q412728\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469890733\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(-7{x}^{3}{y}^{4}\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take each factor to the second power.<\/td>\n<td>[latex]{\\left(-7\\right)}^{2}{\\left({x}^{3}\\right)}^{2}{\\left({y}^{4}\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td>[latex]49{x}^{6}{y}^{8}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146174\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146174&theme=oea&iframe_resize_id=ohm146174&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q625558\">Show Solution<\/span><\/p>\n<div id=\"q625558\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168465997267\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Raise [latex]6n[\/latex] to the second power.<\/td>\n<td>[latex]{6}^{2}{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]36{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property.<\/td>\n<td>[latex]36\\cdot 4\\cdot {n}^{2}\\cdot {n}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the constants and add the exponents.<\/td>\n<td>[latex]144{n}^{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice that in the first monomial, the exponent was outside the parentheses and it applied to both factors inside. In the second monomial, the exponent was inside the parentheses and so it only applied to the <em>n<\/em>.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146177\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146177&theme=oea&iframe_resize_id=ohm146177&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\left(3{p}^{2}q\\right)}^{4}{\\left(2p{q}^{2}\\right)}^{3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q299315\">Show Solution<\/span><\/p>\n<div id=\"q299315\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468310384\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(3{p}^{2}q\\right)}^{4}{\\left(2p{q}^{2}\\right)}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power of a Product Property.<\/td>\n<td>[latex]{3}^{4}{\\left({p}^{2}\\right)}^{4}{q}^{4}\\cdot {2}^{3}{p}^{3}{\\left({q}^{2}\\right)}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td>[latex]81{p}^{8}{q}^{4}\\cdot 8{p}^{3}{q}^{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property.<\/td>\n<td>[latex]81\\cdot 8\\cdot {p}^{8}\\cdot {p}^{3}\\cdot {q}^{4}\\cdot {q}^{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the constants and add the exponents for<\/p>\n<p>each variable.<\/td>\n<td>[latex]648{p}^{11}{q}^{10}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146179\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146179&theme=oea&iframe_resize_id=ohm146179&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Multiply Monomials<\/h3>\n<p>Since a monomial is an algebraic expression, we can use the properties for simplifying expressions with exponents to multiply the monomials.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(4{x}^{2}\\right)\\left(-5{x}^{3}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q762661\">Show Solution<\/span><\/p>\n<div id=\"q762661\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469853450\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(4{x}^{2}\\right)\\left(-5{x}^{3}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange the factors.<\/td>\n<td>[latex]4\\cdot \\left(-5\\right)\\cdot {x}^{2}\\cdot {x}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-20{x}^{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146195\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146195&theme=oea&iframe_resize_id=ohm146195&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(\\Large\\frac{3}{4}\\normalsize{c}^{3}d\\right)\\left(12c{d}^{2}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q867589\">Show Solution<\/span><\/p>\n<div id=\"q867589\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466307238\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(\\Large\\frac{3}{4}\\normalsize{c}^{3}d\\right)\\left(12c{d}^{2}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to rearrange<\/p>\n<p>the factors.<\/td>\n<td>[latex]\\Large\\frac{3}{4}\\normalsize\\cdot 12\\cdot {c}^{3}\\cdot c\\cdot d\\cdot {d}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]9{c}^{4}{d}^{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146196\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146196&theme=oea&iframe_resize_id=ohm146196&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>For more examples of how to use the power and product rules of exponents to simplify and multiply monomials, watch the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 2: Exponent Properties (Product, Power Properties)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/E_D8PO1G7gU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10828\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146196, 146148, 146197. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 2: Exponent Properties (Product, Power Properties). <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/E_D8PO1G7gU\">https:\/\/youtu.be\/E_D8PO1G7gU<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t 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