What is the following sum? 5x(root(x ^ 2 * y, 3)) + 2(root(x ^ 5 * y, 3)) 7x(root(x ^ 2 * y, 6)) \u25cb 7x ^ 2 * (root(x * y ^ 2, 6)) 7x ^ 2 * (root(x * y ^ 2, 3)) 7x(root(x ^ 2 * y, 3))<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The expression you’re working with involves several terms with roots and exponents, making it a bit complex. Let’s first break it down and simplify the parts step by step. The expression is:<\/p>\n\n\n\n [ First, we identify the root and exponent terms involved:<\/p>\n\n\n\n Now, substitute these simplified roots back into the original expression:<\/p>\n\n\n\n [ Let’s break down the multiplication:<\/p>\n\n\n\n Now we combine all the terms together:<\/p>\n\n\n\n [ The terms ( 5x^{5\/3}y^{1\/3} ) and ( 7x^{5\/3}y^{1\/3} ) combine to: Thus, the final expression is:<\/p>\n\n\n\n [ This is the simplified version of the given expression. It combines like terms where possible and reduces the complexity of the original equation. The expression is not easily reducible further unless specific values for ( x ) and ( y ) are given.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the following sum? 5x(root(x ^ 2 * y, 3)) + 2(root(x ^ 5 * y, 3)) 7x(root(x ^ 2 * y, 6)) \u25cb 7x ^ 2 * (root(x * y ^ 2, 6)) 7x ^ 2 * (root(x * y ^ 2, 3)) 7x(root(x ^ 2 * y, 3)) The Correct Answer and […]<\/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-165933","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165933","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=165933"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165933\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165933"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165933"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
5x \\cdot \\sqrt[3]{x^2y} + 2 \\cdot \\sqrt[3]{x^5y} \\cdot 7x \\cdot \\sqrt[6]{x^2y} \\circ 7x^2 \\cdot \\sqrt[6]{xy^2} \\cdot 7x^2 \\cdot \\sqrt[3]{xy^2} \\cdot 7x \\cdot \\sqrt[3]{x^2y}
]<\/p>\n\n\n\nStep 1: Simplifying the terms with roots and exponents<\/h3>\n\n\n\n
\n
[
\\sqrt[3]{x^2y} = x^{2\/3}y^{1\/3}
]<\/li>\n\n\n\n
[
\\sqrt[3]{x^5y} = x^{5\/3}y^{1\/3}
]<\/li>\n\n\n\n
[
\\sqrt[6]{x^2y} = x^{2\/6}y^{1\/6} = x^{1\/3}y^{1\/6}
]<\/li>\n\n\n\n
[
\\sqrt[6]{xy^2} = x^{1\/6}y^{2\/6} = x^{1\/6}y^{1\/3}
]<\/li>\n\n\n\n
[
\\sqrt[3]{xy^2} = x^{1\/3}y^{2\/3}
]<\/li>\n<\/ol>\n\n\n\nStep 2: Substituting into the expression<\/h3>\n\n\n\n
5x \\cdot x^{2\/3}y^{1\/3} + 2 \\cdot x^{5\/3}y^{1\/3} \\cdot 7x \\cdot x^{1\/3}y^{1\/6} \\circ 7x^2 \\cdot x^{1\/6}y^{1\/3} \\cdot 7x^2 \\cdot x^{1\/3}y^{2\/3} \\cdot 7x \\cdot x^{2\/3}y^{1\/3}
]<\/p>\n\n\n\nStep 3: Simplifying terms<\/h3>\n\n\n\n
\n
[
5x^{1+2\/3}y^{1\/3} = 5x^{5\/3}y^{1\/3}
]<\/li>\n\n\n\n
[
2 \\cdot 7 \\cdot x^{5\/3+1}y^{1\/3+1\/6} = 14x^{8\/3}y^{1\/2}
]<\/li>\n\n\n\n
[
7x^{2+1\/6}y^{1\/3} = 7x^{13\/6}y^{1\/3}
]<\/li>\n\n\n\n
[
7x^{2+1\/3}y^{2\/3} = 7x^{7\/3}y^{2\/3}
]<\/li>\n\n\n\n
[
7x^{1+2\/3}y^{1\/3} = 7x^{5\/3}y^{1\/3}
]<\/li>\n<\/ol>\n\n\n\nStep 4: Combining all terms<\/h3>\n\n\n\n
5x^{5\/3}y^{1\/3} + 14x^{8\/3}y^{1\/2} + 7x^{13\/6}y^{1\/3} + 7x^{7\/3}y^{2\/3} + 7x^{5\/3}y^{1\/3}
]<\/p>\n\n\n\n
[
12x^{5\/3}y^{1\/3}
]<\/p>\n\n\n\n
12x^{5\/3}y^{1\/3} + 14x^{8\/3}y^{1\/2} + 7x^{13\/6}y^{1\/3} + 7x^{7\/3}y^{2\/3}
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n