{"id":153843,"date":"2024-10-13T18:42:33","date_gmt":"2024-10-13T18:42:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=153843"},"modified":"2024-10-13T18:42:35","modified_gmt":"2024-10-13T18:42:35","slug":"which-is-equivalent-to-rootindex-3-startroot-8-endroot-superscript-x","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/13\/which-is-equivalent-to-rootindex-3-startroot-8-endroot-superscript-x\/","title":{"rendered":"Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x"},"content":{"rendered":"\n

Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

To find an equivalent expression for (\\sqrt[3]{8^x}), we can break it down step by step.<\/p>\n\n\n\n

Step 1: Simplify the Cube Root<\/h3>\n\n\n\n

The expression (\\sqrt[3]{8^x}) can be rewritten using the exponent rules. The cube root can be expressed as a fractional exponent:
[
\\sqrt[3]{8^x} = (8^x)^{\\frac{1}{3}}
]<\/p>\n\n\n\n

Step 2: Apply the Power of a Power Rule<\/h3>\n\n\n\n

Using the power of a power property ((a^m)^n = a^{m \\cdot n}), we get:
[
(8^x)^{\\frac{1}{3}} = 8^{x \\cdot \\frac{1}{3}} = 8^{\\frac{x}{3}}
]<\/p>\n\n\n\n

Step 3: Express 8 in Terms of Powers<\/h3>\n\n\n\n

Next, we can express 8 as a power of 2. Since (8 = 2^3), we can substitute that into our expression:
[
8^{\\frac{x}{3}} = (2^3)^{\\frac{x}{3}}
]<\/p>\n\n\n\n

Step 4: Simplify Further<\/h3>\n\n\n\n

Again, using the power of a power property:
[
(2^3)^{\\frac{x}{3}} = 2^{3 \\cdot \\frac{x}{3}} = 2^x
]<\/p>\n\n\n\n

Final Result<\/h3>\n\n\n\n

Thus, the expression (\\sqrt[3]{8^x}) simplifies to:
[
\\sqrt[3]{8^x} = 2^x
]<\/p>\n\n\n\n

Conclusion<\/h3>\n\n\n\n

In summary, we started with (\\sqrt[3]{8^x}) and applied the rules of exponents to simplify it step by step. We used the properties of exponents, including the conversion of the cube root to a fractional exponent, the power of a power rule, and the recognition of 8 as a power of 2. Ultimately, we found that (\\sqrt[3]{8^x} = 2^x), making it an equivalent expression that is often simpler and more manageable in further calculations.<\/p>\n","protected":false},"excerpt":{"rendered":"

Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x? The Correct Answer and Explanation is : To find an equivalent expression for (\\sqrt[3]{8^x}), we can break it down step by step. Step 1: Simplify the Cube Root The expression (\\sqrt[3]{8^x}) can be rewritten using the exponent rules. The cube root can be expressed […]<\/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-153843","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153843","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=153843"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153843\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153843"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153843"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}