{"id":4424,"date":"2020-04-13T13:03:46","date_gmt":"2020-04-13T13:03:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4424"},"modified":"2021-02-06T00:05:00","modified_gmt":"2021-02-06T00:05:00","slug":"combining-properties-to-simplify-expressions","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/combining-properties-to-simplify-expressions\/","title":{"raw":"Combining Properties to Simplify Expressions","rendered":"Combining Properties to Simplify Expressions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Simplify quotients that require a combination of the properties of exponents<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe'll now summarize all the properties of exponents so they are all together to refer to as we simplify expressions using several properties. Notice that they are now defined for whole number exponents.\r\n<div class=\"textbox shaded\">\r\n<h3>Summary of Exponent Properties<\/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}\\mathbf{\\text{Product Property}}\\hfill &amp; &amp; &amp; {a}^{m}\\cdot {a}^{n}={a}^{m+n}\\hfill \\\\ \\mathbf{\\text{Power Property}}\\hfill &amp; &amp; &amp; {\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\hfill \\\\ \\mathbf{\\text{Product to a Power Property}}\\hfill &amp; &amp; &amp; {\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\hfill \\\\ \\mathbf{\\text{Quotient Property}}\\hfill &amp; &amp; &amp; \\frac{{a}^{m}}{{a}^{n}}={a}^{m-n},a\\ne 0,m&gt;n\\hfill \\\\ &amp; &amp; &amp; \\frac{{a}^{m}}{{a}^{n}}=\\frac{1}{{a}^{n-m}},a\\ne 0,n&gt;m\\hfill \\\\ \\mathbf{\\text{Zero Exponent Definition}}\\hfill &amp; &amp; &amp; {a}^{0}=1,a\\ne 0\\hfill \\\\ \\mathbf{\\text{Quotient to a Power Property}}\\hfill &amp; &amp; &amp; {\\left(\\frac{a}{b}\\right)}^{m}=\\frac{{a}^{m}}{{b}^{m}},b\\ne 0\\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]{\\Large\\frac{{\\left({x}^{2}\\right)}^{3}}{{x}^{5}}}[\/latex].\r\n\r\nSolution\r\n<table id=\"eip-id1168468505651\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{{\\left({x}^{2}\\right)}^{3}}{{x}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the exponents in the numerator, using the\r\n\r\nPower Property.<\/td>\r\n<td>[latex]{\\Large\\frac{{x}^{6}}{{x}^{5}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the exponents.<\/td>\r\n<td>[latex]x[\/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]146230[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{{m}^{8}}{{\\left({m}^{2}\\right)}^{4}}}[\/latex]\r\n[reveal-answer q=\"680453\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"680453\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468260532\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{{m}^{8}}{{\\left({m}^{2}\\right)}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the exponents in the numerator, using the\r\n\r\nPower Property.<\/td>\r\n<td>[latex]{\\Large\\frac{{m}^{8}}{{m}^{8}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the exponents.<\/td>\r\n<td>[latex]{m}^{0}=1[\/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]146231[\/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({\\Large\\frac{{x}^{7}}{{x}^{3}}}\\right)}^{2}[\/latex]\r\n[reveal-answer q=\"903996\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"903996\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468297399\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left(\\frac{{x}^{7}}{{x}^{3}}\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remember parentheses come before exponents, and the\r\n\r\nbases are the same so we can simplify inside the\r\n\r\nparentheses. Subtract the exponents.<\/td>\r\n<td>[latex]{\\left({x}^{7 - 3}\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\left({x}^{4}\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the exponents.<\/td>\r\n<td>[latex]{x}^{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]146233[\/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({\\Large\\frac{{p}^{2}}{{q}^{5}}}\\right)}^{3}[\/latex]\r\n[reveal-answer q=\"867763\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"867763\"]\r\n\r\nSolution\r\nHere we cannot simplify inside the parentheses first, since the bases are not the same.\r\n<table id=\"eip-id1168467258528\" class=\"unnumbered unstyled\" style=\"width: 859px\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 477.117px\"><\/td>\r\n<td style=\"width: 357.883px\">[latex]{\\Large{\\left(\\frac{{p}^{2}}{{q}^{5}}\\right)}}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 477.117px\">Raise the numerator and denominator to the third power\u00a0using the Quotient to a Power Property, [latex]{\\Large{\\left(\\frac{a}{b}\\right)}}^{m}={\\Large\\frac{{a}^{m}}{{b}^{m}}}[\/latex]<\/td>\r\n<td style=\"width: 357.883px\">[latex]{\\Large\\frac{(p^2)^{3}}{(q^5)^{3}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 477.117px\">Use the Power Property, [latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex].<\/td>\r\n<td style=\"width: 357.883px\">[latex]{\\Large\\frac{{p}^{6}}{{q}^{15}}}[\/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]146234[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large{\\left(\\frac{2{x}^{3}}{3y}\\right)}}^{4}[\/latex]\r\n[reveal-answer q=\"521774\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"521774\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468606012\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large{\\left(\\frac{2{x}^{3}}{3y}\\right)}}^{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Raise the numerator and denominator to the fourth\r\n\r\npower using the Quotient to a Power Property.<\/td>\r\n<td>[latex]{\\Large\\frac{{\\left(2{x}^{3}\\right)}^{4}}{{\\left(3y\\right)}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Raise each factor to the fourth power, using the Power\r\n\r\nto a Power Property.<\/td>\r\n<td>[latex]{\\Large\\frac{{2}^{4}{\\left({x}^{3}\\right)}^{4}}{{3}^{4}{y}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property and simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{16{x}^{12}}{81{y}^{4}}}[\/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]146235[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{{\\left({y}^{2}\\right)}^{3}{\\left({y}^{2}\\right)}^{4}}{{\\left({y}^{5}\\right)}^{4}}}[\/latex]\r\n[reveal-answer q=\"189952\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"189952\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466312387\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{{\\left({y}^{2}\\right)}^{3}{\\left({y}^{2}\\right)}^{4}}{{\\left({y}^{5}\\right)}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Power Property.<\/td>\r\n<td>[latex]{\\Large\\frac{\\left({y}^{6}\\right)\\left({y}^{8}\\right)}{{y}^{20}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the exponents in the numerator, using the Product Property.<\/td>\r\n<td>[latex]{\\Large\\frac{{y}^{14}}{{y}^{20}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Quotient Property.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{{y}^{6}}}[\/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]146893[\/ohm_question]\r\n\r\n[ohm_question]146241[\/ohm_question]\r\n\r\n<\/div>\r\nFor more similar examples, watch the following video.\r\n\r\nhttps:\/\/youtu.be\/Mqx8AXl75UY","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Simplify quotients that require a combination of the properties of exponents<\/li>\n<\/ul>\n<\/div>\n<p>We&#8217;ll now summarize all the properties of exponents so they are all together to refer to as we simplify expressions using several properties. Notice that they are now defined for whole number exponents.<\/p>\n<div class=\"textbox shaded\">\n<h3>Summary of Exponent Properties<\/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}\\mathbf{\\text{Product Property}}\\hfill & & & {a}^{m}\\cdot {a}^{n}={a}^{m+n}\\hfill \\\\ \\mathbf{\\text{Power Property}}\\hfill & & & {\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}\\hfill \\\\ \\mathbf{\\text{Product to a Power Property}}\\hfill & & & {\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\hfill \\\\ \\mathbf{\\text{Quotient Property}}\\hfill & & & \\frac{{a}^{m}}{{a}^{n}}={a}^{m-n},a\\ne 0,m>n\\hfill \\\\ & & & \\frac{{a}^{m}}{{a}^{n}}=\\frac{1}{{a}^{n-m}},a\\ne 0,n>m\\hfill \\\\ \\mathbf{\\text{Zero Exponent Definition}}\\hfill & & & {a}^{0}=1,a\\ne 0\\hfill \\\\ \\mathbf{\\text{Quotient to a Power Property}}\\hfill & & & {\\left(\\frac{a}{b}\\right)}^{m}=\\frac{{a}^{m}}{{b}^{m}},b\\ne 0\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\Large\\frac{{\\left({x}^{2}\\right)}^{3}}{{x}^{5}}}[\/latex].<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468505651\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{{\\left({x}^{2}\\right)}^{3}}{{x}^{5}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents in the numerator, using the<\/p>\n<p>Power Property.<\/td>\n<td>[latex]{\\Large\\frac{{x}^{6}}{{x}^{5}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the exponents.<\/td>\n<td>[latex]x[\/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=\"ohm146230\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146230&theme=oea&iframe_resize_id=ohm146230&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]{\\Large\\frac{{m}^{8}}{{\\left({m}^{2}\\right)}^{4}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q680453\">Show Solution<\/span><\/p>\n<div id=\"q680453\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468260532\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{{m}^{8}}{{\\left({m}^{2}\\right)}^{4}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents in the numerator, using the<\/p>\n<p>Power Property.<\/td>\n<td>[latex]{\\Large\\frac{{m}^{8}}{{m}^{8}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the exponents.<\/td>\n<td>[latex]{m}^{0}=1[\/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=\"ohm146231\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146231&theme=oea&iframe_resize_id=ohm146231&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({\\Large\\frac{{x}^{7}}{{x}^{3}}}\\right)}^{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q903996\">Show Solution<\/span><\/p>\n<div id=\"q903996\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468297399\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\left(\\frac{{x}^{7}}{{x}^{3}}\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remember parentheses come before exponents, and the<\/p>\n<p>bases are the same so we can simplify inside the<\/p>\n<p>parentheses. Subtract the exponents.<\/td>\n<td>[latex]{\\left({x}^{7 - 3}\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\left({x}^{4}\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the exponents.<\/td>\n<td>[latex]{x}^{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=\"ohm146233\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146233&theme=oea&iframe_resize_id=ohm146233&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({\\Large\\frac{{p}^{2}}{{q}^{5}}}\\right)}^{3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q867763\">Show Solution<\/span><\/p>\n<div id=\"q867763\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nHere we cannot simplify inside the parentheses first, since the bases are not the same.<\/p>\n<table id=\"eip-id1168467258528\" class=\"unnumbered unstyled\" style=\"width: 859px\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 477.117px\"><\/td>\n<td style=\"width: 357.883px\">[latex]{\\Large{\\left(\\frac{{p}^{2}}{{q}^{5}}\\right)}}^{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 477.117px\">Raise the numerator and denominator to the third power\u00a0using the Quotient to a Power Property, [latex]{\\Large{\\left(\\frac{a}{b}\\right)}}^{m}={\\Large\\frac{{a}^{m}}{{b}^{m}}}[\/latex]<\/td>\n<td style=\"width: 357.883px\">[latex]{\\Large\\frac{(p^2)^{3}}{(q^5)^{3}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 477.117px\">Use the Power Property, [latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex].<\/td>\n<td style=\"width: 357.883px\">[latex]{\\Large\\frac{{p}^{6}}{{q}^{15}}}[\/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=\"ohm146234\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146234&theme=oea&iframe_resize_id=ohm146234&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]{\\Large{\\left(\\frac{2{x}^{3}}{3y}\\right)}}^{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q521774\">Show Solution<\/span><\/p>\n<div id=\"q521774\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468606012\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large{\\left(\\frac{2{x}^{3}}{3y}\\right)}}^{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Raise the numerator and denominator to the fourth<\/p>\n<p>power using the Quotient to a Power Property.<\/td>\n<td>[latex]{\\Large\\frac{{\\left(2{x}^{3}\\right)}^{4}}{{\\left(3y\\right)}^{4}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Raise each factor to the fourth power, using the Power<\/p>\n<p>to a Power Property.<\/td>\n<td>[latex]{\\Large\\frac{{2}^{4}{\\left({x}^{3}\\right)}^{4}}{{3}^{4}{y}^{4}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property and simplify.<\/td>\n<td>[latex]{\\Large\\frac{16{x}^{12}}{81{y}^{4}}}[\/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=\"ohm146235\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146235&theme=oea&iframe_resize_id=ohm146235&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]{\\Large\\frac{{\\left({y}^{2}\\right)}^{3}{\\left({y}^{2}\\right)}^{4}}{{\\left({y}^{5}\\right)}^{4}}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q189952\">Show Solution<\/span><\/p>\n<div id=\"q189952\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466312387\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{{\\left({y}^{2}\\right)}^{3}{\\left({y}^{2}\\right)}^{4}}{{\\left({y}^{5}\\right)}^{4}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Power Property.<\/td>\n<td>[latex]{\\Large\\frac{\\left({y}^{6}\\right)\\left({y}^{8}\\right)}{{y}^{20}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the exponents in the numerator, using the Product Property.<\/td>\n<td>[latex]{\\Large\\frac{{y}^{14}}{{y}^{20}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Quotient Property.<\/td>\n<td>[latex]{\\Large\\frac{1}{{y}^{6}}}[\/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=\"ohm146893\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146893&theme=oea&iframe_resize_id=ohm146893&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146241\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146241&theme=oea&iframe_resize_id=ohm146241&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>For more similar examples, watch the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Simplify Expressions using Exponent Properties (Quotient \/ Power Properties)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/Mqx8AXl75UY?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-4424\">\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: 146230, 146231, 146233, 146234, 146235, 146893, 146241. <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, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Simplify Expressions using Exponent Properties (Quotient \/ Power Properties). <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Mqx8AXl75UY\">https:\/\/youtu.be\/Mqx8AXl75UY<\/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 <\/section>","protected":false},"author":25777,"menu_order":5,"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 Expressions using Exponent Properties (Quotient \/ Power Properties)\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Mqx8AXl75UY\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146230, 146231, 146233, 146234, 146235, 146893, 146241\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + 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