{"id":146317,"date":"2024-09-30T18:22:51","date_gmt":"2024-09-30T18:22:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=146317"},"modified":"2024-09-30T18:22:53","modified_gmt":"2024-09-30T18:22:53","slug":"which-expression-is-equivalent-to-x1-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/30\/which-expression-is-equivalent-to-x1-3\/","title":{"rendered":"Which expression is equivalent to x1\/3"},"content":{"rendered":"\n

Which expression is equivalent to x1\/3<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The expression ( x^{1\/3} ) is equivalent to the cube root of ( x ), denoted as ( \\sqrt[3]{x} ). This relationship arises from the properties of exponents and roots.<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n
    \n
  1. Understanding Exponents<\/strong>: In mathematics, exponents indicate repeated multiplication. For instance, ( x^2 ) means ( x \\times x ), and ( x^3 ) means ( x \\times x \\times x ). The exponent can also be a fraction, which corresponds to a root. The expression ( x^{1\/n} ) signifies the nth root of ( x ).<\/li>\n\n\n\n
  2. Cube Roots<\/strong>: The cube root of a number is a value that, when multiplied by itself twice (i.e., three times in total), gives the original number. Mathematically, if ( y = \\sqrt[3]{x} ), then ( y^3 = x ). Hence, if we rewrite ( x^{1\/3} ) in root form, we express it as ( \\sqrt[3]{x} ).<\/li>\n\n\n\n
  3. Why Use Fractional Exponents?<\/strong>: The use of fractional exponents can simplify complex calculations and expressions. For example, when simplifying expressions involving powers and roots, having a consistent notation with exponents allows for easier manipulation of equations.<\/li>\n\n\n\n
  4. Properties of Roots and Exponents<\/strong>: Both forms, ( x^{1\/3} ) and ( \\sqrt[3]{x} ), are interchangeable, which can be beneficial in various mathematical contexts. For instance, when solving equations or simplifying algebraic expressions, being able to switch between these forms can make the problem-solving process more straightforward.<\/li>\n\n\n\n
  5. Examples in Practice<\/strong>: If you were to calculate ( x^{1\/3} ) for ( x = 8 ), both ( x^{1\/3} ) and ( \\sqrt[3]{x} ) yield the same result: ( 2 ), since ( 2^3 = 8 ). This shows that understanding both forms is crucial for grasping mathematical concepts related to powers and roots.<\/li>\n<\/ol>\n\n\n\n

    In conclusion, ( x^{1\/3} ) is equivalent to ( \\sqrt[3]{x} ) due to the definitions and properties of exponents and roots. Recognizing this equivalence is fundamental in algebra and helps streamline calculations involving cube roots and fractional exponents.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Which expression is equivalent to x1\/3 The Correct Answer and Explanation is : The expression ( x^{1\/3} ) is equivalent to the cube root of ( x ), denoted as ( \\sqrt[3]{x} ). This relationship arises from the properties of exponents and roots. Explanation In conclusion, ( x^{1\/3} ) is equivalent to ( \\sqrt[3]{x} ) […]<\/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-146317","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146317","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=146317"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/146317\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=146317"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=146317"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=146317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}