{"id":156296,"date":"2022-03-26T01:35:59","date_gmt":"2022-03-25T20:05:59","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/fractional-exponents-explanation-different-functions-and-solved-examples\/"},"modified":"2025-06-23T18:08:20","modified_gmt":"2025-06-23T12:38:20","slug":"fractional-exponents-explanation-different-functions-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/fractional-exponents\/","title":{"rendered":"Fractional Exponents &#8211; Explanation, Different Functions, and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fractional-exponents\/#Introduction_to_Fractional_Exponents\" title=\"Introduction to Fractional Exponents\">Introduction to Fractional Exponents<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fractional-exponents\/#Define_Fractional_Exponent\" title=\"Define Fractional Exponent\">Define Fractional Exponent<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fractional-exponents\/#Fractional_Exponent_Laws\" title=\"Fractional Exponent Laws\">Fractional Exponent Laws<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fractional-exponents\/#How_Negative_Fractional_Exponent_Works\" title=\"How Negative Fractional Exponent Works?\">How Negative Fractional Exponent Works?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/fractional-exponents\/#How_to_Multiply_Fractional_Exponents_With_the_Same_Base\" title=\"How to Multiply Fractional Exponents With the Same Base?\">How to Multiply Fractional Exponents With the Same Base?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Fractional_Exponents\"><\/span>Introduction to Fractional Exponents<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Fractional Exponents &#8211; Explanation Different Functions and Solved Examples.<\/p>\n<p>A fractional exponent is a number that is expressed as a fractional power. For example, the number 3\/2 is a fractional exponent. This number can be written as the following:<\/p>\n<p>3\/2 = (3 \u00d7 2)1\/2<\/p>\n<p>In other words, 3\/2 is equal to 3 raised to the 1\/2 power.<\/p>\n<p>A fractional exponent can also be represented as a radical. For example, the number 3\/2 can also be written as the following:<\/p>\n<p>3\/2 = \u221a(3 \u00d7 2)<\/p>\n<p>This is because the square root of a number is the same as the number raised to the 1\/2 power.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156295 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/fractional-exponents-explanation-different-functions-and-solved-examples.jpg\" alt=\"Fractional Exponents - Explanation, Different Functions, and Solved Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/fractional-exponents-explanation-different-functions-and-solved-examples.jpg?v=1648238755 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/fractional-exponents-explanation-different-functions-and-solved-examples-300x212.jpg?v=1648238755 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Define_Fractional_Exponent\"><\/span>Define Fractional Exponent<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A fractional exponent is a number that is expressed as the power to a power. It is written as the base number raised to a fractional power. For example, the fractional exponent of 2 is 1\/2, which means that the number is raised to the 1\/2 power. The fractional exponent of 3 is 1\/3, which means that the number is raised to the 1\/3 power.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Fractional_Exponent_Laws\"><\/span>Fractional Exponent Laws<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three fractional exponent laws which are used to manipulate fractional exponents.<\/p>\n<p>The first law states that the product of two powers with the same fractional exponent is also a power with that fractional exponent.<\/p>\n<p>For example, if \\(x^{1\/2} \\cdot y^{1\/2} = z^{1\/2}\\), then \\(x = z^{1\/2}\\) and \\(y = z^{1\/2}\\).<\/p>\n<p>The second law states that the quotient of two powers with the same fractional exponent is also a power with that fractional exponent.<\/p>\n<p>For example, if \\(x^{1\/2} \\div y^{1\/2} = z^{1\/2}\\), then \\(x = z^{1\/2}\\) and \\(y = 0\\).<\/p>\n<p>The third law states that the power to a power with a fractional exponent is the same power with that fractional exponent.<\/p>\n<p>For example, if \\(x^{1\/2}^3 = z^{1\/2}\\), then \\(x = z^{1\/2}\\).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_Negative_Fractional_Exponent_Works\"><\/span>How Negative Fractional Exponent Works?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A negative fractional exponent is used to define a power that is less than 1. In physics, this is known as a &#8220;decaying exponential.&#8221; In mathematical terms, a negative fractional exponent can be written as:<\/p>\n<p>a-n = 1\/(1+n)<\/p>\n<p>For example, if we want to calculate the value of a-0.5, we would use the following equation:<\/p>\n<p>1\/(1+0.5) = 1\/1.5 = 0.667<\/p>\n<p>This means that a-0.5 is equal to 0.667, or 66.7%.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Multiply_Fractional_Exponents_With_the_Same_Base\"><\/span>How to Multiply Fractional Exponents With the Same Base?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics, multiplying fractional exponents with the same base is a very simple process. To do this, all you have to do is add the exponents together. For example, if you have the fractional exponent 3\/2, you would simply add the exponents together to get 5\/2. This is because 3\/2 is equal to 1.5, and 5\/2 is equal to 2.5.<\/p>\n<p>There are a few things to keep in mind when multiplying fractional exponents with the same base. First, the base must be the same for both exponents. Second, you must make sure that the fractions are in the same form. Lastly, the exponents must be integers.<\/p>\n<p>If you are multiplying fractional exponents with different bases, you must convert the bases to the same base before multiplying the exponents. For example, if you are multiplying the fractional exponent 3\/4 and the fractional exponent 2\/5, you would first convert 3\/4 to 12\/16 and 2\/5 to 10\/25. After converting the bases, you would then add the exponents together to get 22\/25. Fractional Exponents &#8211; Explanation, Different Functions, and Solved Examples.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Fractional Exponents Fractional Exponents &#8211; Explanation Different Functions and Solved Examples. 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