{"id":218383,"date":"2025-05-23T17:33:37","date_gmt":"2025-05-23T17:33:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218383"},"modified":"2025-05-23T17:33:40","modified_gmt":"2025-05-23T17:33:40","slug":"what-is-the-cube-root-of-729a9b6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/23\/what-is-the-cube-root-of-729a9b6\/","title":{"rendered":"what is the cube root of -729a9b6"},"content":{"rendered":"\n

what is the cube root of -729a9<\/sup>b6<\/sup><\/p>\n\n\n\n

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

Correct Answer:<\/h3>\n\n\n\n

The cube root of \u2212729a9b6-729a^9b^6 is: \u22129a3b2\\boxed{-9a^3b^2}<\/p>\n\n\n\n

\n\n\n\n

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

To find the cube root of an expression like \u2212729a9b6-729a^9b^6, we apply the cube root to each factor separately, using the property: xyz3=x3\u22c5y3\u22c5z3\\sqrt[3]{xyz} = \\sqrt[3]{x} \\cdot \\sqrt[3]{y} \\cdot \\sqrt[3]{z}<\/p>\n\n\n\n

Step 1: Cube root of the constant<\/h4>\n\n\n\n

\u2212729-729 is a negative number. The cube root of a negative number is negative (since (\u2212a)3=\u2212a3(-a)^3 = -a^3). Now, find the cube root of 729: 729=93so7293=9729 = 9^3 \\quad \\text{so} \\quad \\sqrt[3]{729} = 9<\/p>\n\n\n\n

Thus, \u22127293=\u22129\\sqrt[3]{-729} = -9<\/p>\n\n\n\n

Step 2: Cube root of a9a^9<\/h4>\n\n\n\n

For exponents, we use the rule: a93=a9\/3=a3\\sqrt[3]{a^9} = a^{9\/3} = a^3<\/p>\n\n\n\n

Step 3: Cube root of b6b^6<\/h4>\n\n\n\n

Similarly, b63=b6\/3=b2\\sqrt[3]{b^6} = b^{6\/3} = b^2<\/p>\n\n\n\n

Step 4: Combine the results<\/h4>\n\n\n\n

Now combine all cube roots: \u2212729a9b63=\u22127293\u22c5a93\u22c5b63=\u22129\u22c5a3\u22c5b2=\u22129a3b2\\sqrt[3]{-729a^9b^6} = \\sqrt[3]{-729} \\cdot \\sqrt[3]{a^9} \\cdot \\sqrt[3]{b^6} = -9 \\cdot a^3 \\cdot b^2 = \\boxed{-9a^3b^2}<\/p>\n\n\n\n

Summary:<\/h4>\n\n\n\n

This simplification uses basic properties of cube roots and exponents:<\/p>\n\n\n\n

    \n
  • xn3=xn\/3\\sqrt[3]{x^n} = x^{n\/3}<\/li>\n\n\n\n
  • The cube root of a negative number is negative.<\/li>\n\n\n\n
  • Cube roots distribute over multiplication.<\/li>\n<\/ul>\n\n\n\n

    So the cube root of the entire expression \u2212729a9b6-729a^9b^6 is \u22129a3b2\\boxed{-9a^3b^2}.<\/p>\n\n\n\n

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

    what is the cube root of -729a9b6 The Correct Answer and Explanation is: Correct Answer: The cube root of \u2212729a9b6-729a^9b^6 is: \u22129a3b2\\boxed{-9a^3b^2} To find the cube root of an expression like \u2212729a9b6-729a^9b^6, we apply the cube root to each factor separately, using the property: xyz3=x3\u22c5y3\u22c5z3\\sqrt[3]{xyz} = \\sqrt[3]{x} \\cdot \\sqrt[3]{y} \\cdot \\sqrt[3]{z} Step 1: Cube root […]<\/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-218383","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218383","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=218383"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218383\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}