{"id":2202,"date":"2021-06-11T05:32:43","date_gmt":"2021-06-11T05:32:43","guid":{"rendered":"https:\/\/phelixinfosolutions.com\/blog\/?p=2202"},"modified":"2021-11-15T05:01:16","modified_gmt":"2021-11-15T05:01:16","slug":"how-to-perform-multiplication-of-exponents","status":"publish","type":"post","link":"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/","title":{"rendered":"How to Perform Multiplication of Exponents?"},"content":{"rendered":"<div class=\"47de946b8831610645f1873afb8597bb\" data-index=\"4\" style=\"float: none; margin:10px 0 10px 0; text-align:center;\">\n<script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-0205282431111794\"\r\n     crossorigin=\"anonymous\"><\/script>\r\n<!-- 2024 Vertical -->\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:block\"\r\n     data-ad-client=\"ca-pub-0205282431111794\"\r\n     data-ad-slot=\"3037936695\"\r\n     data-ad-format=\"auto\"\r\n     data-full-width-responsive=\"true\"><\/ins>\r\n<script>\r\n     (adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\n<\/div>\n<p>Exponents are an important part of algebra that forms the foundation of higher-level math studies like polynomial equations. Unfortunately, many students often struggle to understand and work with them. To master the vital skill of multiplying <a href=\"https:\/\/www.cuemath.com\/algebra\/exponents\/\">exponents<\/a> it is important to go learn about the basics of exponents, their types, and rules so that it is convenient to apply them. Let\u2019s begin with learning about exponents, their type, rules, and multiplication of exponents.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_69_1 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69fb9b847cce9\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69fb9b847cce9\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/#Exponents_Types_Rules\" title=\"Exponents, Types &amp; Rules\">Exponents, Types &amp; Rules<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/#4_Ways_to_Multiply_Exponents\" title=\"4 Ways to Multiply Exponents\">4 Ways to Multiply Exponents<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/#Multiplying_Exponents_with_the_Same_Base\" title=\"Multiplying Exponents with the Same Base\">Multiplying Exponents with the Same Base<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/#Multiplying_Exponents_With_Different_Bases\" title=\"Multiplying Exponents With Different Bases\">Multiplying Exponents With Different Bases<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/#Multiplying_Exponents_With_Different_Bases_and_Exponents\" title=\"Multiplying Exponents With Different Bases and Exponents\">Multiplying Exponents With Different Bases and Exponents<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/#Multiplying_Negative_Exponents\" title=\"Multiplying Negative Exponents\">Multiplying Negative Exponents<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Exponents_Types_Rules\"><\/span>Exponents, Types &amp; Rules<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Exponents are the value that shows how many times a base number will multiply by itself. The number raised by power is known as the base, while the superscript number above it is the exponent or power.\u00a0 Types of exponents are positive exponents, negative exponents, zero exponents, and rational exponents.<\/p>\n<p>Positive exponents are simplified just by multiplying the base to itself the number of times indicated by the exponent\/power. <a href=\"https:\/\/www.cuemath.com\/algebra\/negative-exponents\/\">Negative exponents<\/a> or the negative sign of an exponent means the reciprocal. You can simplify a negative exponent by using its fractional form where one represents its numerator and base with power represents the denominator. Zero exponents are expressions with the exponent as 0, and there is no need to consider the base value during simplification. Rational or fractional exponents will become radical or roots. For example, 31\/3 can be written as 3root of 3, 65\/2 can be written as two root (or square root) of 6 raises to the power 5. For learning exponent multiplications, it is important to know the 7 exponent rules. Let\u2019s review them below:<\/p>\n<ul>\n<li><strong>Product of powers rule:<\/strong> When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.<\/li>\n<li><strong>The quotient of powers rules:<\/strong> Multiplication and division are opposites of each other, much the same, the quotient rule acts as the opposite of the product rule.<\/li>\n<li><strong>Power of a power rule:<\/strong> This rule shows how to solve equations where power is being raised by another power. When dividing two bases of the same value, keep the base the same and subtract the exponent values.<\/li>\n<li><strong>Power of a product rule:<\/strong> When any base is being multiplied by an exponent, distribute the exponent to each part of the base.<\/li>\n<li><strong>Power of a quotient rule:<\/strong> A quotient simply means that you\u2019re dividing two quantities. In this rule, you\u2019re raising a quotient by a power. Like the power of a product rule, the exponent needs to be distributed to all values within the brackets it\u2019s attached to.<\/li>\n<li><strong>Zero power rule:<\/strong> Any base raised to the power of zero is equal to one.<\/li>\n<li><strong>Negative exponent rule:<\/strong> When a number has a negative exponent, flip it into a reciprocal to turn the exponent into a positive exponent. Don\u2019t use the negative exponent to turn the base into a negative.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"4_Ways_to_Multiply_Exponents\"><\/span>4 Ways to Multiply Exponents<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Here are four strategies that are simple shortcuts to simplify complicated equations. In order to find the actual value of an <a href=\"https:\/\/www.allmath.com\/exponents.php\">exponent<\/a>, students must first understand what it means: repeated multiplication.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Multiplying_Exponents_with_the_Same_Base\"><\/span>Multiplying Exponents with the Same Base<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>When you\u2019re multiplying exponents, use the first rule: add powers together when multiplying like bases. For example, to find the product of 4^2 \u00d7 4^6, the bases of the equation stay the same, and the values of the exponents get added together.<\/p>\n<p>That is, 4^2 \u00d7 4^6 = 4^8<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Multiplying_Exponents_With_Different_Bases\"><\/span>Multiplying Exponents With Different Bases<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>It is possible to multiply exponents with different bases, but it requires the exponents to be the same. For example, to simplify\u00a0 4^2 \u00d7 2^2 = ? first multiply the bases together and then, add the exponent. Instead of adding the two exponents together, keep it the same.<\/p>\n<p>4^2 \u00d7 2^2 = 6^4 = 1296<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Multiplying_Exponents_With_Different_Bases_and_Exponents\"><\/span>Multiplying Exponents With Different Bases and Exponents<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Multiplying different exponents with different bases is not possible. For example, 2^2 and 3^3 have nothing in common to combine, we can\u2019t simplify them down into a single exponent and it should be expressed as a regular number.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Multiplying_Negative_Exponents\"><\/span>Multiplying Negative Exponents<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Multiplying exponents with negative powers may seem a little tricky but it is exactly the same as multiplying exponents with non-negative powers.<\/p>\n<p>Learning about the properties of negative numbers will enable students to comfortably work with negative numbers before learning the multiplication of negative exponents. The main thing is to remember the exponent rule to change a negative exponent into a positive one by flipping it into a reciprocal. Then use the same above-mentioned ways to solve them.<\/p>\n\n<div style=\"font-size: 0px; height: 0px; line-height: 0px; margin: 0; padding: 0; clear: both;\"><\/div>","protected":false},"excerpt":{"rendered":"<p>Exponents are an important part of algebra that forms the foundation of higher-level math studies like polynomial equations. Unfortunately, many students often struggle to understand and work with them. To master the vital skill of multiplying exponents it is important to go learn about the basics of exponents, their types, and rules so that it [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2203,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[90],"tags":[3319,3315,3322,3316,3321,3320,3318,3317],"class_list":["post-2202","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-other","tag-dividing-exponents-with-different-bases","tag-multiplication-of-exponents","tag-multiplying-exponents-calculator-multiplying-negative-exponents","tag-multiplying-exponents-with-different-bases","tag-multiplying-exponents-with-different-bases-worksheets","tag-multiplying-exponents-with-parentheses","tag-multiplying-exponents-with-same-base","tag-multiplying-variables-with-exponents"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v18.7 (Yoast SEO v23.9) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to Perform Multiplication of Exponents? | Phelix Info Solution Tech Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Perform Multiplication of Exponents?\" \/>\n<meta property=\"og:description\" content=\"Exponents are an important part of algebra that forms the foundation of higher-level math studies like polynomial equations. 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| Phelix Info Solution Tech Blog","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/phelixinfosolutions.com\/blog\/how-to-perform-multiplication-of-exponents\/","og_locale":"en_US","og_type":"article","og_title":"How to Perform Multiplication of Exponents?","og_description":"Exponents are an important part of algebra that forms the foundation of higher-level math studies like polynomial equations. Unfortunately, many students often struggle to understand and work with them. 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