{"id":239287,"date":"2025-07-02T19:28:51","date_gmt":"2025-07-02T19:28:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=239287"},"modified":"2025-07-02T19:28:54","modified_gmt":"2025-07-02T19:28:54","slug":"value-of-81-to-the-power-of-1-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/02\/value-of-81-to-the-power-of-1-2\/","title":{"rendered":"value of 81 to the power of – 1\/2"},"content":{"rendered":"\n

value of 81 to the power of – 1\/2<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The value of 81\u22121281^{-\\frac{1}{2}} is 19\\frac{1}{9}.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To solve this, let’s break it down into smaller steps.<\/p>\n\n\n\n

The expression 81\u22121281^{-\\frac{1}{2}} can be understood as a two-part operation:<\/p>\n\n\n\n

    \n
  1. Negative exponent<\/strong>: A negative exponent means you take the reciprocal of the base raised to the positive version of the exponent. In other words, a\u2212n=1ana^{-n} = \\frac{1}{a^n}. So, 81\u221212=1811281^{-\\frac{1}{2}} = \\frac{1}{81^{\\frac{1}{2}}}.<\/li>\n\n\n\n
  2. Fractional exponent<\/strong>: The exponent 12\\frac{1}{2} represents the square root of the base. For any number aa, a12a^{\\frac{1}{2}} is equivalent to a\\sqrt{a}. Therefore, 8112=8181^{\\frac{1}{2}} = \\sqrt{81}, and since the square root of 81 is 9, we have: 8112=981^{\\frac{1}{2}} = 9.<\/li>\n<\/ol>\n\n\n\n

    Now, putting it all together: 81\u221212=18112=1981^{-\\frac{1}{2}} = \\frac{1}{81^{\\frac{1}{2}}} = \\frac{1}{9}<\/p>\n\n\n\n

    So, the value of 81\u22121281^{-\\frac{1}{2}} is 19\\frac{1}{9}. This shows the relationship between negative exponents and square roots.<\/p>\n","protected":false},"excerpt":{"rendered":"

    value of 81 to the power of – 1\/2 The correct answer and explanation is: The value of 81\u22121281^{-\\frac{1}{2}} is 19\\frac{1}{9}. Explanation: To solve this, let’s break it down into smaller steps. The expression 81\u22121281^{-\\frac{1}{2}} can be understood as a two-part operation: Now, putting it all together: 81\u221212=18112=1981^{-\\frac{1}{2}} = \\frac{1}{81^{\\frac{1}{2}}} = \\frac{1}{9} So, the value […]<\/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-239287","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/239287","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=239287"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/239287\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=239287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=239287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=239287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}