{"id":8465,"date":"2017-05-25T19:09:51","date_gmt":"2017-05-25T19:09:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=8465"},"modified":"2020-10-22T09:29:33","modified_gmt":"2020-10-22T09:29:33","slug":"divide-monomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/divide-monomials\/","title":{"raw":"12.3.a - Dividing Monomials","rendered":"12.3.a &#8211; Dividing Monomials"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Divide monomials<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Divide Monomials<\/h2>\r\nIn the previous module we reviewed all the properties of exponents. We will now use them to divide monomials. Later, you will use them to divide polynomials.\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nFind the quotient: [latex]56{x}^{5}\\div 7{x}^{2}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168466176948\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]56{x}^{5}\\div 7{x}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.2px\">\r\n<td style=\"height: 15.2px\">Rewrite as a fraction.<\/td>\r\n<td style=\"height: 15.2px\">[latex]{\\dfrac{56{x}^{5}}{7{x}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 74px\">\r\n<td style=\"height: 74px\">Use fraction multiplication to separate the number\r\n\r\npart from the variable part.<\/td>\r\n<td style=\"height: 74px\">[latex]{\\dfrac{56}{7}}\\cdot {\\dfrac{{x}^{5}}{{x}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Use the Quotient Property.<\/td>\r\n<td style=\"height: 15px\">[latex]8{x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\nFind the quotient: [latex]63{x}^{8}\\div 9{x}^{4}[\/latex]\r\n\r\n[reveal-answer q=\"980543\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"980543\"]\r\n\r\n[latex]7{x}^{4}[\/latex]<sup>\u00a0<\/sup>\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nFind the quotient: [latex]96{y}^{11}\\div 6{y}^{8}[\/latex]\r\n\r\n[reveal-answer q=\"245633\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"245633\"]\r\n\r\n[latex]16{y}^{3}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]186447[\/ohm_question]\r\n\r\n<\/div>\r\nWhen we divide monomials with more than one variable, we write one fraction for each variable.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the quotient: [latex]{\\dfrac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168467383069\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\dfrac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use fraction multiplication.<\/td>\r\n<td>[latex]{\\dfrac{42}{-7}}\\cdot {\\dfrac{{x}^{2}}{x}}\\cdot {\\dfrac{{y}^{3}}{{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify and use the Quotient Property.<\/td>\r\n<td>[latex]-6\\cdot x\\cdot {\\dfrac{1}{{y}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-{\\dfrac{6x}{{y}^{2}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\nFind the quotient: [latex]{\\dfrac{-84{x}^{8}{y}^{3}}{7{x}^{10}{y}^{2}}}[\/latex]\r\n\r\n[reveal-answer q=\"881156\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"881156\"]\r\n\r\n[latex]-{\\dfrac{12y}{{x}^{2}}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nFind the quotient: [latex]{\\dfrac{-72{a}^{4}{b}^{5}}{-8{a}^{9}{b}^{5}}}[\/latex]\r\n\r\n[reveal-answer q=\"432765\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"432765\"]\r\n\r\n[latex]{\\dfrac{9}{{a}^{5}}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nFind the quotient: [latex]{\\dfrac{24{a}^{5}{b}^{3}}{48a{b}^{4}}}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168466706076\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\dfrac{24{a}^{5}{b}^{3}}{48a{b}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use fraction multiplication.<\/td>\r\n<td>[latex]{\\dfrac{24}{48}}\\cdot {\\dfrac{{a}^{5}}{a}}\\cdot {\\dfrac{{b}^{3}}{{b}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify and use the Quotient Property.<\/td>\r\n<td>[latex]{\\dfrac{1}{2}}\\cdot {a}^{4}\\cdot {\\dfrac{1}{b}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]{\\dfrac{{a}^{4}}{2b}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\nFind the quotient: [latex]{\\dfrac{16{a}^{7}{b}^{6}}{24a{b}^{8}}}[\/latex]\r\n\r\n[reveal-answer q=\"712712\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"712712\"]\r\n\r\n[latex]{\\dfrac{2{a}^{6}}{3{b}^{2}}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nFind the quotient: [latex]{\\dfrac{27{p}^{4}{q}^{7}}{-45{p}^{12}{q}^{}}}[\/latex]\r\n\r\n[reveal-answer q=\"338809\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"338809\"]\r\n\r\n[latex]-{\\dfrac{3{q}^{6}}{5{p}^{8}}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nOnce you become familiar with the process and have practiced it step by step several times, you may be able to simplify a fraction in one step.\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nFind the quotient: [latex]{\\dfrac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168469859213\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\dfrac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify and use the Quotient Property.<\/td>\r\n<td>[latex]{\\dfrac{2{y}^{6}}{3{x}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\nBe very careful to simplify [latex]{\\dfrac{14}{21}}[\/latex] by dividing out a common factor, and to simplify the variables by subtracting their exponents.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\nFind the quotient: [latex]{\\dfrac{28{x}^{5}{y}^{14}}{49{x}^{9}{y}^{12}}}[\/latex]\r\n\r\n[reveal-answer q=\"277668\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"277668\"]\r\n\r\n[latex]{\\dfrac{4{y}^{2}}{7{x}^{4}}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nFind the quotient: [latex]{\\dfrac{30{m}^{5}{n}^{11}}{48{m}^{10}{n}^{14}}}[\/latex]\r\n\r\n[reveal-answer q=\"673456\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"673456\"]\r\n\r\n[latex]{\\dfrac{5}{8{m}^{5}{n}^{3}}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn all examples so far, there was no work to do in the numerator or denominator before simplifying the fraction. In the next example, we'll first find the product of two monomials in the numerator before we simplify the fraction.\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nFind the quotient: [latex]{\\dfrac{(3{x}^{3}{y}^{2})(10{x}^{2}{y}^{3})}{6{x}^{4}{y}^{5}}}[\/latex]\r\n\r\nSolution\r\nRemember, the fraction bar is a grouping symbol. We will simplify the numerator first.\r\n<table id=\"eip-id1168469828864\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\dfrac{\\left(3{x}^{3}{y}^{2}\\right)\\left(10{x}^{2}{y}^{3}\\right)}{6{x}^{4}{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator.<\/td>\r\n<td>[latex]{\\dfrac{30{x}^{5}{y}^{5}}{6{x}^{4}{y}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify, using the Quotient Rule.<\/td>\r\n<td>[latex]5x[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\nFind the quotient: [latex]{\\Large\\frac{\\left(3{x}^{4}{y}^{5}\\right)\\left(8{x}^{2}{y}^{5}\\right)}{12{x}^{5}{y}^{8}}}[\/latex]\r\n\r\n[reveal-answer q=\"909087\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"909087\"]\r\n\r\n[latex]2{xy}^{2}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nFind the quotient: [latex]{\\Large\\frac{\\left(-6{a}^{6}{b}^{9}\\right)\\left(-8{a}^{5}{b}^{8}\\right)}{-12{a}^{10}{b}^{12}}}[\/latex]\r\n\r\n[reveal-answer q=\"872244\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"872244\"]\r\n\r\n[latex]-4{ab}^{5}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]199935[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Divide monomials<\/li>\n<\/ul>\n<\/div>\n<h2>Divide Monomials<\/h2>\n<p>In the previous module we reviewed all the properties of exponents. We will now use them to divide monomials. Later, you will use them to divide polynomials.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Find the quotient: [latex]56{x}^{5}\\div 7{x}^{2}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466176948\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]56{x}^{5}\\div 7{x}^{2}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.2px\">\n<td style=\"height: 15.2px\">Rewrite as a fraction.<\/td>\n<td style=\"height: 15.2px\">[latex]{\\dfrac{56{x}^{5}}{7{x}^{2}}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 74px\">\n<td style=\"height: 74px\">Use fraction multiplication to separate the number<\/p>\n<p>part from the variable part.<\/td>\n<td style=\"height: 74px\">[latex]{\\dfrac{56}{7}}\\cdot {\\dfrac{{x}^{5}}{{x}^{2}}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Use the Quotient Property.<\/td>\n<td style=\"height: 15px\">[latex]8{x}^{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>Find the quotient: [latex]63{x}^{8}\\div 9{x}^{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q980543\">Show Solution<\/span><\/p>\n<div id=\"q980543\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]7{x}^{4}[\/latex]<sup>\u00a0<\/sup><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Find the quotient: [latex]96{y}^{11}\\div 6{y}^{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q245633\">Show Solution<\/span><\/p>\n<div id=\"q245633\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]16{y}^{3}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm186447\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=186447&theme=oea&iframe_resize_id=ohm186447&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>When we divide monomials with more than one variable, we write one fraction for each variable.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467383069\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\dfrac{42{x}^{2}{y}^{3}}{-7x{y}^{5}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use fraction multiplication.<\/td>\n<td>[latex]{\\dfrac{42}{-7}}\\cdot {\\dfrac{{x}^{2}}{x}}\\cdot {\\dfrac{{y}^{3}}{{y}^{5}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td>[latex]-6\\cdot x\\cdot {\\dfrac{1}{{y}^{2}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-{\\dfrac{6x}{{y}^{2}}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{-84{x}^{8}{y}^{3}}{7{x}^{10}{y}^{2}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q881156\">Show Solution<\/span><\/p>\n<div id=\"q881156\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]-{\\dfrac{12y}{{x}^{2}}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Find the quotient: [latex]{\\dfrac{-72{a}^{4}{b}^{5}}{-8{a}^{9}{b}^{5}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q432765\">Show Solution<\/span><\/p>\n<div id=\"q432765\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]{\\dfrac{9}{{a}^{5}}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{24{a}^{5}{b}^{3}}{48a{b}^{4}}}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466706076\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\dfrac{24{a}^{5}{b}^{3}}{48a{b}^{4}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use fraction multiplication.<\/td>\n<td>[latex]{\\dfrac{24}{48}}\\cdot {\\dfrac{{a}^{5}}{a}}\\cdot {\\dfrac{{b}^{3}}{{b}^{4}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td>[latex]{\\dfrac{1}{2}}\\cdot {a}^{4}\\cdot {\\dfrac{1}{b}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]{\\dfrac{{a}^{4}}{2b}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{16{a}^{7}{b}^{6}}{24a{b}^{8}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q712712\">Show Solution<\/span><\/p>\n<div id=\"q712712\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]{\\dfrac{2{a}^{6}}{3{b}^{2}}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Find the quotient: [latex]{\\dfrac{27{p}^{4}{q}^{7}}{-45{p}^{12}{q}^{}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q338809\">Show Solution<\/span><\/p>\n<div id=\"q338809\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]-{\\dfrac{3{q}^{6}}{5{p}^{8}}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Once you become familiar with the process and have practiced it step by step several times, you may be able to simplify a fraction in one step.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469859213\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\dfrac{14{x}^{7}{y}^{12}}{21{x}^{11}{y}^{6}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify and use the Quotient Property.<\/td>\n<td>[latex]{\\dfrac{2{y}^{6}}{3{x}^{4}}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>Be very careful to simplify [latex]{\\dfrac{14}{21}}[\/latex] by dividing out a common factor, and to simplify the variables by subtracting their exponents.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{28{x}^{5}{y}^{14}}{49{x}^{9}{y}^{12}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q277668\">Show Solution<\/span><\/p>\n<div id=\"q277668\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]{\\dfrac{4{y}^{2}}{7{x}^{4}}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Find the quotient: [latex]{\\dfrac{30{m}^{5}{n}^{11}}{48{m}^{10}{n}^{14}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q673456\">Show Solution<\/span><\/p>\n<div id=\"q673456\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]{\\dfrac{5}{8{m}^{5}{n}^{3}}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In all examples so far, there was no work to do in the numerator or denominator before simplifying the fraction. In the next example, we&#8217;ll first find the product of two monomials in the numerator before we simplify the fraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Find the quotient: [latex]{\\dfrac{(3{x}^{3}{y}^{2})(10{x}^{2}{y}^{3})}{6{x}^{4}{y}^{5}}}[\/latex]<\/p>\n<p>Solution<br \/>\nRemember, the fraction bar is a grouping symbol. We will simplify the numerator first.<\/p>\n<table id=\"eip-id1168469828864\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\dfrac{\\left(3{x}^{3}{y}^{2}\\right)\\left(10{x}^{2}{y}^{3}\\right)}{6{x}^{4}{y}^{5}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator.<\/td>\n<td>[latex]{\\dfrac{30{x}^{5}{y}^{5}}{6{x}^{4}{y}^{5}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify, using the Quotient Rule.<\/td>\n<td>[latex]5x[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>Find the quotient: [latex]{\\Large\\frac{\\left(3{x}^{4}{y}^{5}\\right)\\left(8{x}^{2}{y}^{5}\\right)}{12{x}^{5}{y}^{8}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q909087\">Show Solution<\/span><\/p>\n<div id=\"q909087\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]2{xy}^{2}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Find the quotient: [latex]{\\Large\\frac{\\left(-6{a}^{6}{b}^{9}\\right)\\left(-8{a}^{5}{b}^{8}\\right)}{-12{a}^{10}{b}^{12}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q872244\">Show Solution<\/span><\/p>\n<div id=\"q872244\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]-4{ab}^{5}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm199935\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=199935&theme=oea&iframe_resize_id=ohm199935&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-8465\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Simplify Fractions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/_2Wk7jXf3Ok\">https:\/\/youtu.be\/_2Wk7jXf3Ok<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Simplify Exponential Expressions Using the Power Property of Exponents. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Hgu9HKDHTUA\">https:\/\/youtu.be\/Hgu9HKDHTUA<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 146014, 146148. <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>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/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 <\/section>","protected":false},"author":21,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex 1: Simplify Fractions\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/_2Wk7jXf3Ok\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Simplify Exponential Expressions Using the Power Property of Exponents\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Hgu9HKDHTUA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 146014, 146148\",\"author\":\"Lumen 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