{"id":2926,"date":"2024-02-09T20:24:23","date_gmt":"2024-02-09T20:24:23","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/?post_type=chapter&#038;p=2926"},"modified":"2026-03-11T19:17:52","modified_gmt":"2026-03-11T19:17:52","slug":"9-4-1-multiplication-of-monomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/9-4-1-multiplication-of-monomials\/","title":{"raw":"9.4.1: Multiplication of Monomials","rendered":"9.4.1: Multiplication of Monomials"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h1>Learning Outcomes<\/h1>\r\n<ul>\r\n \t<li>Multiply monomials<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h1>Key words<\/h1>\r\n<ul>\r\n \t<li><strong>Product<\/strong>: the answer when two or more terms are multiplied<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Properties of Exponents<\/h2>\r\nWe learned about and used properties for multiplying expressions with exponents in chapter 1. Let\u2019s summarize them here, then we\u2019ll show 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<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<h4>Solution<\/h4>\r\n<table id=\"eip-id1168467221786\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 533.612px;\" colspan=\"2\">Simplifying [latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 233.744px;\"><\/td>\r\n<td style=\"width: 288.706px;\">[latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 233.744px;\">Use the Power Property: multiply exponents<\/td>\r\n<td style=\"width: 288.706px;\">[latex]{x}^{12}\\cdot {x}^{20}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 233.744px;\">Use the Product Property: add the exponents.<\/td>\r\n<td style=\"width: 288.706px;\">[latex]{x}^{32}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\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<h4>Solution<\/h4>\r\n<table id=\"eip-id1168469890733\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<th colspan=\"2\">Simplifying [latex]{\\left(-7{x}^{3}{y}^{4}\\right)}^{2}[\/latex]<\/th>\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: multiply the exponents<\/td>\r\n<td>[latex]49{x}^{6}{y}^{8}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\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<h4>Solution<\/h4>\r\n<table id=\"eip-id1168465997267\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 493.962px;\" colspan=\"2\">Simplifying [latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 234.394px;\"><\/td>\r\n<td style=\"width: 248.406px;\">[latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 234.394px;\">Raise [latex]6n[\/latex] to the second power.<\/td>\r\n<td style=\"width: 248.406px;\">[latex]{6}^{2}{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 234.394px;\">Simplify.<\/td>\r\n<td style=\"width: 248.406px;\">[latex]36{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 234.394px;\">Use the Commutative Property.<\/td>\r\n<td style=\"width: 248.406px;\">[latex]36\\cdot 4\\cdot {n}^{2}\\cdot {n}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 234.394px;\">Multiply the constants and add the exponents.<\/td>\r\n<td style=\"width: 248.406px;\">[latex]144{n}^{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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 [latex]n[\/latex].\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<h4>Solution<\/h4>\r\n<table id=\"eip-id1168468310384\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<th colspan=\"2\">Simplifying [latex]{\\left(3{p}^{2}q\\right)}^{4}{\\left(2p{q}^{2}\\right)}^{3}[\/latex]<\/th>\r\n<\/tr>\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>\r\n<p class=\"no-indent\">Multiply the constants and add the exponents for each variable.<\/p>\r\n<\/td>\r\n<td>[latex]648{p}^{11}{q}^{10}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\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><\/h3>\r\n<h3>Multiplying Monomials<\/h3>\r\nIn math, we build on concepts we have already learned. Since a monomial is an algebraic term, we can use the properties for simplifying expressions with exponents to multiply 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<h4>Solution<\/h4>\r\n<table id=\"eip-id1168469853450\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<th colspan=\"2\">[latex]\\left(4{x}^{2}\\right)\\left(-5{x}^{3}\\right)[\/latex]<\/th>\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<\/div>\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\nFind the product of [latex]\\left(\\frac{3}{4}{c}^{3}d\\right)\\text{ and }\\left(12c{d}^{2}\\right)[\/latex]\r\n<h4>Solution<\/h4>\r\n<table id=\"eip-id1168466307238\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<th style=\"width: 669.237px;\" colspan=\"2\">Multiplying [latex]\\left(\\frac{3}{4}{c}^{3}d\\right)\\text{ and }\\left(12c{d}^{2}\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 310.362px;\"><\/td>\r\n<td style=\"width: 347.712px;\">[latex]\\left(\\frac{3}{4}{c}^{3}d\\right)\\left(12c{d}^{2}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 310.362px;\">Use the Commutative Property to rearrange\r\n\r\nthe factors.<\/td>\r\n<td style=\"width: 347.712px;\">[latex]\\frac{3}{4}\\cdot 12\\cdot {c}^{3}\\cdot c\\cdot d\\cdot {d}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 310.362px;\">Multiply.<\/td>\r\n<td style=\"width: 347.712px;\">[latex]9{c}^{4}{d}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\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\n&nbsp;\r\n\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\r\n\r\n<a href=\"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-content\/uploads\/sites\/5676\/2024\/02\/Transcript-9.4.1-1.docx\">Transcript-9.4.1-1<\/a>","rendered":"<div class=\"textbox learning-objectives\">\n<h1>Learning Outcomes<\/h1>\n<ul>\n<li>Multiply monomials<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h1>Key words<\/h1>\n<ul>\n<li><strong>Product<\/strong>: the answer when two or more terms are multiplied<\/li>\n<\/ul>\n<\/div>\n<h2>Properties of Exponents<\/h2>\n<p>We learned about and used properties for multiplying expressions with exponents in chapter 1. Let\u2019s summarize them here, then we\u2019ll show 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<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<h4>Solution<\/h4>\n<table id=\"eip-id1168467221786\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<th style=\"width: 533.612px;\" colspan=\"2\">Simplifying [latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 233.744px;\"><\/td>\n<td style=\"width: 288.706px;\">[latex]{\\left({x}^{2}\\right)}^{6}{\\left({x}^{5}\\right)}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 233.744px;\">Use the Power Property: multiply exponents<\/td>\n<td style=\"width: 288.706px;\">[latex]{x}^{12}\\cdot {x}^{20}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 233.744px;\">Use the Product Property: add the exponents.<\/td>\n<td style=\"width: 288.706px;\">[latex]{x}^{32}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\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<h4>Solution<\/h4>\n<table id=\"eip-id1168469890733\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<th colspan=\"2\">Simplifying [latex]{\\left(-7{x}^{3}{y}^{4}\\right)}^{2}[\/latex]<\/th>\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: multiply the exponents<\/td>\n<td>[latex]49{x}^{6}{y}^{8}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\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<h4>Solution<\/h4>\n<table id=\"eip-id1168465997267\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<th style=\"width: 493.962px;\" colspan=\"2\">Simplifying [latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 234.394px;\"><\/td>\n<td style=\"width: 248.406px;\">[latex]{\\left(6n\\right)}^{2}\\left(4{n}^{3}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 234.394px;\">Raise [latex]6n[\/latex] to the second power.<\/td>\n<td style=\"width: 248.406px;\">[latex]{6}^{2}{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 234.394px;\">Simplify.<\/td>\n<td style=\"width: 248.406px;\">[latex]36{n}^{2}\\cdot 4{n}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 234.394px;\">Use the Commutative Property.<\/td>\n<td style=\"width: 248.406px;\">[latex]36\\cdot 4\\cdot {n}^{2}\\cdot {n}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 234.394px;\">Multiply the constants and add the exponents.<\/td>\n<td style=\"width: 248.406px;\">[latex]144{n}^{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 [latex]n[\/latex].<\/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<h4>Solution<\/h4>\n<table id=\"eip-id1168468310384\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<th colspan=\"2\">Simplifying [latex]{\\left(3{p}^{2}q\\right)}^{4}{\\left(2p{q}^{2}\\right)}^{3}[\/latex]<\/th>\n<\/tr>\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>\n<p class=\"no-indent\">Multiply the constants and add the exponents for each variable.<\/p>\n<\/td>\n<td>[latex]648{p}^{11}{q}^{10}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\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><\/h3>\n<h3>Multiplying Monomials<\/h3>\n<p>In math, we build on concepts we have already learned. Since a monomial is an algebraic term, we can use the properties for simplifying expressions with exponents to multiply 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<h4>Solution<\/h4>\n<table id=\"eip-id1168469853450\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<th colspan=\"2\">[latex]\\left(4{x}^{2}\\right)\\left(-5{x}^{3}\\right)[\/latex]<\/th>\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 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>Find the product of [latex]\\left(\\frac{3}{4}{c}^{3}d\\right)\\text{ and }\\left(12c{d}^{2}\\right)[\/latex]<\/p>\n<h4>Solution<\/h4>\n<table id=\"eip-id1168466307238\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<th style=\"width: 669.237px;\" colspan=\"2\">Multiplying [latex]\\left(\\frac{3}{4}{c}^{3}d\\right)\\text{ and }\\left(12c{d}^{2}\\right)[\/latex]<\/th>\n<\/tr>\n<tr>\n<td style=\"width: 310.362px;\"><\/td>\n<td style=\"width: 347.712px;\">[latex]\\left(\\frac{3}{4}{c}^{3}d\\right)\\left(12c{d}^{2}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 310.362px;\">Use the Commutative Property to rearrange<\/p>\n<p>the factors.<\/td>\n<td style=\"width: 347.712px;\">[latex]\\frac{3}{4}\\cdot 12\\cdot {c}^{3}\\cdot c\\cdot d\\cdot {d}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 310.362px;\">Multiply.<\/td>\n<td style=\"width: 347.712px;\">[latex]9{c}^{4}{d}^{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\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>&nbsp;<\/p>\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<p><a 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