{"id":278222,"date":"2025-08-01T21:10:17","date_gmt":"2025-08-01T21:10:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=278222"},"modified":"2025-08-01T21:10:20","modified_gmt":"2025-08-01T21:10:20","slug":"the-expression-above-can-also-be-written-in-the-form-sqrtcab","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/01\/the-expression-above-can-also-be-written-in-the-form-sqrtcab\/","title":{"rendered":"The expression above can also be written in the form sqrt[c](a^b)"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

Answer:<\/strong>
For this expression, a = 7<\/strong>, b = 2<\/strong>, and c = 9<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

The problem requires converting an expression with a fractional exponent into its equivalent radical form. The original expression given is 7 raised to the power of 2\/9, which is written as 7^(2\/9). The goal is to represent this in the form c\u221a(a^b) and identify the corresponding values of a, b, and c.<\/p>\n\n\n\n

The fundamental rule for converting between fractional exponents and radicals is:
x^(m\/n) = n\u221a(x^m)<\/p>\n\n\n\n

In this formula:<\/p>\n\n\n\n

    \n
  • x<\/strong>\u00a0is the base.<\/li>\n\n\n\n
  • m<\/strong>\u00a0is the numerator of the fractional exponent, which becomes the power of the base inside the radical.<\/li>\n\n\n\n
  • n<\/strong>\u00a0is the denominator of the fractional exponent, which becomes the index, or root, of the radical.<\/li>\n<\/ul>\n\n\n\n

    Let’s apply this rule to the given expression, 7^(2\/9).
    First, we identify the components of our expression in relation to the general formula:<\/p>\n\n\n\n

      \n
    • The base,\u00a0x<\/strong>, is 7.<\/li>\n\n\n\n
    • The numerator of the exponent,\u00a0m<\/strong>, is 2.<\/li>\n\n\n\n
    • The denominator of the exponent,\u00a0n<\/strong>, is 9.<\/li>\n<\/ul>\n\n\n\n

      Now, we substitute these values into the radical form n\u221a(x^m):<\/p>\n\n\n\n

        \n
      • The denominator,\u00a0n = 9<\/strong>, becomes the index of the root.<\/li>\n\n\n\n
      • The base,\u00a0x = 7<\/strong>, is placed inside the radical sign.<\/li>\n\n\n\n
      • The numerator,\u00a0m = 2<\/strong>, becomes the exponent of the base inside the radical.<\/li>\n<\/ul>\n\n\n\n

        Following this substitution, the expression 7^(2\/9) is rewritten as 9\u221a(7^2).<\/p>\n\n\n\n

        Finally, we compare this result, 9\u221a(7^2), to the target form provided in the problem, c\u221a(a^b).
        By matching the parts of the two expressions:<\/p>\n\n\n\n

          \n
        • a<\/strong>, the base inside the radical, corresponds to\u00a07<\/strong>.<\/li>\n\n\n\n
        • b<\/strong>, the exponent inside the radical, corresponds to\u00a02<\/strong>.<\/li>\n\n\n\n
        • c<\/strong>, the index of the root, corresponds to\u00a09<\/strong>.<\/li>\n<\/ul>\n\n\n\n

          Therefore, the correct values are a = 7, b = 2, and c = 9.<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          The correct answer and explanation is: Answer:For this expression, a = 7, b = 2, and c = 9. Explanation The problem requires converting an expression with a fractional exponent into its equivalent radical form. The original expression given is 7 raised to the power of 2\/9, which is written as 7^(2\/9). The goal is to represent this […]<\/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-278222","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278222","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=278222"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/278222\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=278222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=278222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=278222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}