{"id":12739,"date":"2014-01-31T21:18:08","date_gmt":"2014-01-31T21:18:08","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=12739"},"modified":"2026-03-26T09:55:51","modified_gmt":"2026-03-26T14:55:51","slug":"laws-of-exponents","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/laws-of-exponents\/","title":{"rendered":"Laws of Exponents"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass__amLIP8cF0U\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage__amLIP8cF0U\" data-source-videoID=\"_amLIP8cF0U\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Laws of Exponents Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Laws of Exponents\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage__amLIP8cF0U:hover {cursor:pointer;} img#videoThumbnailImage__amLIP8cF0U {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-laws-of-exponents-64bec48866528-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage__amLIP8cF0U\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage__amLIP8cF0U\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Laws of Exponents\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass__amLIP8cF0U\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass__amLIP8cF0U\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage__amLIP8cF0U\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction T64_Function() {\n  var x = document.getElementById(\"T64\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"T64_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"T64\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Product_of_Powers\" class=\"smooth-scroll\">Product of Powers<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Quotient_of_Powers\" class=\"smooth-scroll\">Quotient of Powers<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Power_of_a_Power\" class=\"smooth-scroll\">Power of a Power<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Power_of_a_Product\" class=\"smooth-scroll\">Power of a Product<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Power_of_Quotient\" class=\"smooth-scroll\">Power of Quotient<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Frequently_Asked_Questions\" class=\"smooth-scroll\">Frequently Asked Questions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Laws_of_Exponents_PDF\" class=\"smooth-scroll\">Laws of Exponents PDF<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Laws_of_Exponents_Practice_Questions\" class=\"smooth-scroll\">Laws of Exponents Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"FAQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"FAQs\">FAQs<\/label><input id=\"factsheet\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"factsheet\">Fact Sheet<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, and welcome to this video on the laws of exponents!<\/p>\n<p>Working with <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/intro-to-polynomials\/\">polynomial<\/a>, radical, and rational functions often times requires us to perform algebraic operations with powers. Recall that a power is nothing more than a base that is raised to an <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/exponents\/\">exponent<\/a>.<\/p>\n<p>Let\u2019s take a look at the properties of exponents that are used to simplify algebraic expressions with powers. <\/p>\n<h2><span id=\"Product_of_Powers\" class=\"m-toc-anchor\"><\/span>Product of Powers<\/h2>\n<p>\nThe product of powers property applies to powers with the same base. When asked to multiply powers with the same base, simply add the exponents. For example:<\/p>\n<div class=\"examplesentence\">\\(b^2 \\times b^3 = b^5 \\)<\/div>\n<p>\n&nbsp;<br \/>\nThis rule makes intuitive sense if you expand each power like this:<\/p>\n<div class=\"examplesentence\">\\((b\\cdot b)(b\\cdot b\\cdot b)\\)<\/div>\n<p>\n&nbsp;<br \/>\nCounting up the bases of \\(b\\) that are being multiplied results in 5.<\/p>\n<div class=\"examplesentence\">\\((b\\cdot b)(b\\cdot b\\cdot b)=b^{5}\\)<\/div>\n<p>\n&nbsp;<br \/>\nTherefore, the general form of the product of powers rule is:<\/p>\n<div class=\"examplesentence\">\\(b^mb^n =  b^{(m+n)} \\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Quotient_of_Powers\" class=\"m-toc-anchor\"><\/span>Quotient of Powers<\/h2>\n<p>\nThe quotient of powers property also applies to powers with the same base; however, the rule requires the subtraction of exponents. Let\u2019s look at an example:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{b^5}{b^3}\\) <span style=\"font-size: 90%;\"> in expanded form would look like <\/span> \\(\\frac{b \\cdot b \\cdot b \\cdot b \\cdot b}{b \\cdot b \\cdot b }\\)<\/div>\n<p>\n&nbsp;<br \/>\nCanceling out common factors of \\(b\\) from the numerator and the denominator would simplify to be \\(b^2\\).  <\/p>\n<p>The quotient of powers property allows a quicker, more efficient result. Simply subtract the exponent of the denominator from the exponent of the numerator: \\(5-3=2\\).<\/p>\n<p>The general form for quotient of powers property is:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\(\\frac{b^m}{b^n} = b^{(m-n)}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Power_of_a_Power\" class=\"m-toc-anchor\"><\/span>Power of a Power<\/h2>\n<p>\nThe power of a power property allows us to raise a power to another exponent. Once again, expanding an expression makes understanding the rule a bit easier. Suppose the power \\(b^3\\) is squared:<\/p>\n<div class=\"examplesentence\">\\((b^3)^2\\)<\/div>\n<p>\n&nbsp;<br \/>\nIn expanded form it would look like this: \\((b\\cdot  b\\cdot b)(b\\cdot b\\cdot b)\\). Using the product of powers property, or simply counting up the bases of \\(b\\), results in \\(b^6\\).  <\/p>\n<p>The general form of this property is:<\/p>\n<div class=\"examplesentence\">\\((b^m)^n=b^{mn}\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Power_of_a_Product\" class=\"m-toc-anchor\"><\/span>Power of a Product<\/h2>\n<p>\nExpanding on the power of a power property results in additional tools that are used to simplify expressions with powers.<\/p>\n<p>For example, suppose the base of a power is a monomial with a coefficient and a variable.  <\/p>\n<p>\\((3b^4)^2\\) expands to \\((3b^4)(3b^4)\\). Rearranging the factors to group the coefficients and the powers with the same base, \\(b\\), and simplifying gives us \\((3 \\cdot  3 \\cdot  b^4 \\cdot  b^4)=9b^8\\).<\/p>\n<p>This is called the power of a product property and illustrates that the exponent of each factor in the base must be multiplied by the power outside the parentheses. <\/p>\n<p>The general form for the power of product property is:<\/p>\n<div class=\"examplesentence\">\\((b \\cdot c)^x=b^x \\cdot c^x\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Power_of_Quotient\" class=\"m-toc-anchor\"><\/span>Power of Quotient<\/h2>\n<p>\nThe power of quotient property is similar in that the exponent of a rational base is multiplied by the exponents in both the numerator and denominator. Let\u2019s look at some examples:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\((\\frac{b^3}{c^2})^2\\) <span style=\"font-size: 90%;\">&nbsp;expands to<\/span> \\((\\frac{b^3}{c^2})(\\frac{b^3}{c^2})\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe product of powers property results in the simplified expression <span style=\"font-size:130%\">\\(\\frac{b^{6}}{c^{4}}\\)<\/span>.<\/p>\n<p>However, applying the power of quotient property directly is often more efficient:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\((\\frac{b^3}{c^2})^2 = \\frac{b^{3 \\cdot 2}}{c^{2 \\cdot 2}} = \\frac{b^6}{c^4}\\)<\/div>\n<p>\n&nbsp;<br \/>\nHere\u2019s another example:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\">\\((\\frac{2b}{c^2d})^3\\) <span style=\"font-size: 90%;\">&nbsp;expands to<\/span> \\((\\frac{2b}{c^2d})(\\frac{2b}{c^2d})(\\frac{2b}{c^2d})\\)<\/div>\n<p>\n&nbsp;<br \/>\nRearranging factors and applying the product of powers property results in:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{2 \\cdot 2 \\cdot 2 \\cdot b \\cdot b\\cdot b}{c^2 \\cdot c^2 \\cdot c^2 \\cdot d \\cdot d \\cdot d} = \\frac{8b^3}{c^6d^3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nIf we were to apply the power of quotient property, it would look like this:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\((\\frac{2^{1 \\cdot 3}b^{1 \\cdot 3}}{c^{2 \\cdot 3}d^{1 \\cdot 3}}) = \\frac{2^3b^3}{c^6d^3} = \\frac{8b^3}{c^6d^3}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe general rule for the power of quotient property is:  <\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\((\\frac{b}{c})^x = \\frac{b^x}{c^x}\\)<\/div>\n<p>\n&nbsp;<br \/>\nAs you can see, these rules are essential in simplifying expressions within our work with various algebraic functions.  <\/p>\n<p>Thanks for watching this review covering the laws of exponents! Happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"FAQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Frequently_Asked_Questions\" class=\"m-toc-anchor\"><\/span>Frequently Asked Questions<\/h2>\n<div class=\"faq-list\">\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the formula for product of powers?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The product of powers rule says that when multiplying exponents with the same base, you can find the product by keeping the base and adding the exponents. <\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Find the product of \\(x^4\u00b7x^3\\)<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\">To solve, keep the base \\(x\\) and add the exponents. <\/p>\n<p style=\"text-align: center\">\\(x^4\u00b7x^3=x^4+3=x^7\\)<\/p>\n<p style=\"margin-bottom: 0em\">The rule works because when we expand each term, we get \\((x\u00b7x\u00b7x\u00b7x)\u00b7(x\u00b7x\u00b7x)\\), which is equivalent to \\(x^7\\).<\/p>\n<\/div>\n<p>The general formula that is used to represent this rule is \\(a^m\u00b7a^n=a^{m+n}\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the product of powers property?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The product of powers property states that when multiplying exponents with the same base, you find the product by keeping the base and adding the exponents.<\/p>\n<p>The formula for the rule is \\(a^m\u00b7a^n=a^{m+n}\\). For example, the \\(w^5\\times w^7=w^{5+7}=w^{12}\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is an example of quotient of powers?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The quotient of powers rule states that when dividing exponents with the same base, we keep the base and subtract the exponents. The general formula for the rule is \\(a^m\\div a^n=a^{m-n}\\).<\/p>\n<p>An example of the quotient of powers is \\(x^8\\div x^3=x^{8-3}=x^5\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the quotient rule for exponents?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The quotient rule for exponents says that when dividing exponents with the same base, we keep the base and subtract the exponents. The general form of the rule is \\(a^m\\div a^n=a^{m-n}\\).<\/p>\n<p>For example, to find the quotient of \\(y^{11}\\div y^4\\), we keep the base and subtract the exponents to get \\(y^7\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">Can you have a power of a power?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>Yes, you can have a power of a power. The power of a power rule says that when a number with an exponent is raised to another exponent, we can simplify the exponent by keeping the base and multiplying the exponents. The general form of the rule is \\((a^m)^n=a^{m\u00b7n}\\).<\/p>\n<p>For example, to find the power of the power of the expression, \\((x^2)^7=x^{2 \\cdot 7}=x^{14}\\).<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the power of power rule in math?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The power of power rule states that when a number with an exponent is raised to another exponent, the expression can be simplified by keeping the base and multiplying the exponents. The general form of the rule is \\((a^m)^n=a^{m\u00b7n}\\).<\/p>\n<p>You can see why the rule works when you expand the exponents.<\/p>\n<div class=\"lightbulb-example-2\"><span class=\"lightbulb-icon\">\ud83d\udca1<\/span><span class=\"faq-example-question\">Example: Expand the expression \\((y^3)^2\\).<\/span><\/p>\n<hr style=\"padding: 0; margin-top: -0.2em; margin-bottom: 1.2em\"> Inside the parentheses, expand \\(y^3\\) to \\((y \\cdot y \\cdot y)^2\\). Now, raise the expression inside the parentheses to the second power: \\(y \\cdot y \\cdot y \\cdot y \\cdot y \\cdot y\\). As you can see, this is equivalent to \\(y^6\\).<\/p>\n<p>If we apply the rule, we get the following: <\/p>\n<p style=\"text-align: center; margin-bottom: 0em\">\\((y^3)^2=y^{3 \\cdot 2}=y^6\\)<\/p>\n<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the power of product property?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The power of product property or rule states that if two numbers multiplied by one another are raised to a certain power, then each number is raised to that power and then the numbers are multiplied. The general form of the rule is \\((ab)^m=a^mb^m\\).<br \/><Br>For example, to simplify the expression \\((3x)^3\\), we raise each term inside the parentheses to the third power and then simplify:<\/p>\n<p style=\"text-align: center\">\\((3x)^3=3^3x^3=27x^3\\)<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<div class=\"qa_wrap\">\n<div class=\"q_item text_bold\">\n<h4 class=\"letter\">Q<\/h4>\n<p style=\"line-height: unset;\">What is the power of quotient property?<\/p>\n<\/p><\/div>\n<div class=\"a_item\">\n<h4 class=\"letter text_bold\">A<\/h4>\n<p>The power of quotient property states that if two numbers divided by one another are raised to a certain power, then each number is raised to that power and then the numbers are divided. The general form of the rule is \\((\\frac{a}{b})^m=\\frac{a^m}{b^m}\\).<\/p>\n<p>For example, to simplify the expression \\((\\frac{2}{4})^3\\), we raise each number to the third power and then divide: <\/p>\n<p style=\"text-align: center\">\\((\\dfrac{2}{4})^3=\\dfrac{2^3}{4^3}=\\dfrac{8}{64}=\\dfrac{1}{8}\\)<\/p>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"factsheet-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Laws_of_Exponents_PDF\" class=\"m-toc-anchor\"><\/span>Laws of Exponents PDF<\/h2>\n<div>\n\t\t\t\t\t<img width=\"1354\" height=\"1764\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_100212.png\" class=\"attachment-full size-full\" alt=\"An infographic describing the properties of exponents, including the product of powers, quotient of powers, power of a power, power of a product, and power of a quotient properties.\" decoding=\"async\" loading=\"lazy\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_100212.png 1354w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_100212-230x300.png 230w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_100212-786x1024.png 786w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_100212-768x1001.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/image_2022-01-07_100212-1179x1536.png 1179w\" sizes=\"auto, (max-width: 1354px) 100vw, 1354px\" \/><\/p>\n<div class=\"sub_categories\">\n\t\t\t\t\t\t<a href=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/01\/Properties-of-Exponents-Fact-Sheet.pdf\"><span id=\"Your_Laws_of_Exponents_PDF_Download\" class=\"m-toc-anchor\"><\/span>Your Laws of Exponents PDF Download<\/a>\n\t\t\t\t\t<\/div>\n<\/p>\n<\/div>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Laws_of_Exponents_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Laws of Exponents Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(x^2 \\times x^5=\\) ?<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(x^{10}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(x^9\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(x^8\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">\\(x^7\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>According to the product of powers property, when two numbers with the same base are multiplied together, the base will stay the same and the exponents are added:<\/p>\n<p style=\"text-align: center\">\\(x^2 \\times x^5=x^{(2+5)}=x^7\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\(y^6 \\div y^3=\\) ?<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(y^3\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(y^2\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(y\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(y^5\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>According to the quotient of powers property, when two numbers with the same base are divided, the base will stay the same and the exponents will be subtracted:<\/p>\n<p style=\"text-align: center\">\\(y^6 \\div y^3=y^{(6-3)}=y^3\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve the following equation:<\/p>\n<div class=\"yellow-math-quote\">\\((z^2 )^8=\\) ?<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">\\(z^{16}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(z^{10}\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(z^8\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(z^{12}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>According to the power of a power property, when a number with an exponent is raised to a power, the base stays the same and the exponents are multiplied:<\/p>\n<p style=\"text-align: center\">\\((z^2 )^8=z^{(2 \\times 8)}=z^{16}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich of the following is a correct statement?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\((6 \\times4)^2\\) \\(\\:=6^2+4^2\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\((3 \\times 7)^6\\) \\(\\:=21^6+7^6\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">\\((7 \\times 9)^3\\) \\(\\:=7^3 \\times 9^3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\((4 \\times 2)^5\\) \\(=4^5-2^5\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>This is an example of the power of product property, which says:<\/p>\n<p style=\"text-align: center\">\\((b\u00d7c)^x=b^x\u00d7c^x\\)<\/p>\n<p>In other words, when two numbers are multiplied together and then raised to a power, it is the same as saying the first number raised to the power times the second number raised to the power.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich of the following statements is not true?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\((x\u00d7y)^3=x^3 y^3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\((\\dfrac{x^3}{y^2})^4=\\dfrac{x^7}{y^6}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\((x^5)^4=x^{20}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(y^7 \\times y^9=y^{16}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>According to the power of a power property, the correct statement for Choice B <em>should<\/em> be the following:<\/p>\n<p style=\"text-align: center\">\\((\\dfrac{x^3}{y^2})^4=\\dfrac{x^{12}}{y^8}\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/basic-arithmetic\/\">Return to Basic Arithmetic Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Basic Arithmetic 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