{"id":168207,"date":"2024-11-16T20:37:27","date_gmt":"2024-11-16T20:37:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168207"},"modified":"2024-11-16T20:37:30","modified_gmt":"2024-11-16T20:37:30","slug":"simplify-the-following-expression","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/16\/simplify-the-following-expression\/","title":{"rendered":"Simplify the following expression."},"content":{"rendered":"\n

Select the correct answer.<\/strong>Simplify the following expression.

\"3^{(11)\/(5)}

A. 12
B. 81
C.\u00a0\"(1)\/(81)\"
D.\u00a0\"(1)\/(12)\"<\/p>\n\n\n\n

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

The given expression is:<\/p>\n\n\n\n

[
\\frac{3^{\\frac{11}{5}}}{3^{-\\frac{2}{5}}}
]<\/p>\n\n\n\n

Step 1: Apply the quotient rule for exponents<\/h3>\n\n\n\n

The quotient rule for exponents states that:<\/p>\n\n\n\n

[
\\frac{a^m}{a^n} = a^{m-n}
]<\/p>\n\n\n\n

In this case, the base is 3, so we apply this rule to subtract the exponents:<\/p>\n\n\n\n

[
\\frac{3^{\\frac{11}{5}}}{3^{-\\frac{2}{5}}} = 3^{\\frac{11}{5} – \\left(-\\frac{2}{5}\\right)} = 3^{\\frac{11}{5} + \\frac{2}{5}}
]<\/p>\n\n\n\n

Step 2: Simplify the exponent<\/h3>\n\n\n\n

Now, simplify the exponent:<\/p>\n\n\n\n

[
\\frac{11}{5} + \\frac{2}{5} = \\frac{11 + 2}{5} = \\frac{13}{5}
]<\/p>\n\n\n\n

Thus, the expression becomes:<\/p>\n\n\n\n

[
3^{\\frac{13}{5}}
]<\/p>\n\n\n\n

Step 3: Interpret the result<\/h3>\n\n\n\n

The expression ( 3^{\\frac{13}{5}} ) means we are raising 3 to the power of ( \\frac{13}{5} ). This is equivalent to:<\/p>\n\n\n\n

[
3^{\\frac{13}{5}} = \\left( 3^{13} \\right)^{\\frac{1}{5}}
]<\/p>\n\n\n\n

This means we first calculate ( 3^{13} ), then take the fifth root of that result.<\/p>\n\n\n\n

Step 4: Calculate ( 3^{13} )<\/h3>\n\n\n\n

First, calculate ( 3^{13} ):<\/p>\n\n\n\n

[
3^{13} = 1594323
]<\/p>\n\n\n\n

Now, take the fifth root of 1594323. The fifth root of 1594323 is approximately 12.<\/p>\n\n\n\n

Thus:<\/p>\n\n\n\n

[
3^{\\frac{13}{5}} \\approx 12
]<\/p>\n\n\n\n

Step 5: Conclusion<\/h3>\n\n\n\n

Therefore, the correct answer is:<\/p>\n\n\n\n

[
\\boxed{12}
]<\/p>\n\n\n\n

This result comes from applying the exponent rules and simplifying the expression step by step.<\/p>\n","protected":false},"excerpt":{"rendered":"

Select the correct answer.Simplify the following expression. A. 12B. 81C.\u00a0D.\u00a0 The Correct Answer and Explanation is: The given expression is: [\\frac{3^{\\frac{11}{5}}}{3^{-\\frac{2}{5}}}] Step 1: Apply the quotient rule for exponents The quotient rule for exponents states that: [\\frac{a^m}{a^n} = a^{m-n}] In this case, the base is 3, so we apply this rule to subtract the exponents: […]<\/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-168207","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168207","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=168207"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168207\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}