{"id":156505,"date":"2024-10-17T10:48:24","date_gmt":"2024-10-17T10:48:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156505"},"modified":"2024-10-17T10:48:26","modified_gmt":"2024-10-17T10:48:26","slug":"write-x3-4-in-radical-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/write-x3-4-in-radical-form\/","title":{"rendered":"Write x3\/4 in radical form"},"content":{"rendered":"\n<p>Write x3\/4 in radical form<\/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 express ( x^{3\/4} ) in radical form, we can utilize the properties of exponents and radicals. The expression ( x^{3\/4} ) can be rewritten as follows:<\/p>\n\n\n\n<p>[<br>x^{3\/4} = \\left( x^3 \\right)^{1\/4}<br>]<\/p>\n\n\n\n<p>This indicates that we are taking the fourth root of ( x^3 ). In radical notation, this is expressed as:<\/p>\n\n\n\n<p>[<br>x^{3\/4} = \\sqrt[4]{x^3}<br>]<\/p>\n\n\n\n<p>To further clarify this transformation, let\u2019s break it down step by step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Understanding Exponents<\/strong>: The fraction ( \\frac{3}{4} ) in the exponent can be separated into two parts: the numerator (3) and the denominator (4). The numerator indicates that we will be dealing with ( x^3 ), while the denominator indicates the root we will be taking.<\/li>\n\n\n\n<li><strong>Applying the Radical<\/strong>: When you have an exponent expressed as ( \\frac{m}{n} ), it translates to ( x^m ) being taken to the ( n )-th root. So, for our case, ( m = 3 ) and ( n = 4 ).<\/li>\n\n\n\n<li><strong>Radical Notation<\/strong>: The notation ( \\sqrt[n]{x^m} ) is a way to express roots. Therefore, ( x^{3\/4} = \\sqrt[4]{x^3} ) fits perfectly with our understanding of exponents and radicals.<\/li>\n\n\n\n<li><strong>Visualizing the Concept<\/strong>: If ( x ) were a specific number, ( x^{3\/4} ) represents a value that is both a power and a root of ( x ). For instance, if ( x = 16 ), then ( x^{3\/4} = \\sqrt[4]{16^3} = \\sqrt[4]{4096} = 6.3496 ) (approximately).<\/li>\n<\/ol>\n\n\n\n<p>In conclusion, the radical form of ( x^{3\/4} ) is ( \\sqrt[4]{x^3} ). This transformation highlights the relationship between exponents and roots, providing a different perspective on how to manipulate and understand expressions involving fractional exponents.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write x3\/4 in radical form The Correct Answer and Explanation is : To express ( x^{3\/4} ) in radical form, we can utilize the properties of exponents and radicals. The expression ( x^{3\/4} ) can be rewritten as follows: [x^{3\/4} = \\left( x^3 \\right)^{1\/4}] This indicates that we are taking the fourth root of ( [&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-156505","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156505","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=156505"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156505\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}