{"id":146445,"date":"2024-10-01T05:44:38","date_gmt":"2024-10-01T05:44:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146445"},"modified":"2024-10-01T05:44:40","modified_gmt":"2024-10-01T05:44:40","slug":"what-is-1-2-to-the-4th-power-as-a-fraction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/01\/what-is-1-2-to-the-4th-power-as-a-fraction\/","title":{"rendered":"What is 1\/2 to the 4th power as a fraction"},"content":{"rendered":"\n<p>What is 1\/2 to the 4th power as a fraction?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate ( \\left(\\frac{1}{2}\\right)^4 ), we can follow the rules of exponents. When we raise a fraction to a power, we raise both the numerator and the denominator to that power. Thus, we can express this as follows:<\/p>\n\n\n\n<p>[<br>\\left(\\frac{1}{2}\\right)^4 = \\frac{1^4}{2^4}<br>]<\/p>\n\n\n\n<p>Next, we calculate ( 1^4 ) and ( 2^4 ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( 1^4 = 1 ) (because any number raised to any power remains the same when the number is one).<\/li>\n\n\n\n<li>( 2^4 = 2 \\times 2 \\times 2 \\times 2 ).<\/li>\n<\/ul>\n\n\n\n<p>Calculating ( 2^4 ):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( 2 \\times 2 = 4 )<\/li>\n\n\n\n<li>( 4 \\times 2 = 8 )<\/li>\n\n\n\n<li>( 8 \\times 2 = 16 )<\/li>\n<\/ol>\n\n\n\n<p>So, ( 2^4 = 16 ).<\/p>\n\n\n\n<p>Now, substituting these values back into the fraction, we have:<\/p>\n\n\n\n<p>[<br>\\left(\\frac{1}{2}\\right)^4 = \\frac{1}{16}<br>]<\/p>\n\n\n\n<p>Thus, ( \\left(\\frac{1}{2}\\right)^4 ) simplifies to ( \\frac{1}{16} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The process of raising a fraction to a power involves understanding the properties of exponents. The key rule to remember is that ( (a\/b)^n = a^n \/ b^n ). This means that the numerator and denominator are both raised to the same exponent.<\/p>\n\n\n\n<p>In this case, the base fraction ( \\frac{1}{2} ) has a numerator of 1 and a denominator of 2. By applying the exponent of 4, we calculated ( 1^4 ) and ( 2^4 ) separately.<\/p>\n\n\n\n<p>Raising a number to the power of 4 involves multiplying that number by itself four times. For example, ( 2^4 ) is calculated through sequential multiplication, which helps in understanding the concept of powers and the growth of numbers as they are multiplied.<\/p>\n\n\n\n<p>The result, ( \\frac{1}{16} ), indicates that when the fraction ( \\frac{1}{2} ) is multiplied by itself four times, it results in a much smaller value, demonstrating how exponential decay works in fractions. Hence, the final answer is:<\/p>\n\n\n\n<p>[<br>\\left(\\frac{1}{2}\\right)^4 = \\frac{1}{16}<br>]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is 1\/2 to the 4th power as a fraction? The Correct Answer and Explanation is : To calculate ( \\left(\\frac{1}{2}\\right)^4 ), we can follow the rules of exponents. When we raise a fraction to a power, we raise both the numerator and the denominator to that power. Thus, we can express this as follows: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-146445","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146445","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=146445"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146445\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146445"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146445"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146445"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}