Simplify.
216^1\/3<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To simplify 2161\/3216^{1\/3}2161\/3, we are asked to find the cube root of 216. This means we need to determine which number, when multiplied by itself three times (cubed), gives 216.<\/p>\n\n\n\n The cube root of a number xxx, denoted x1\/3x^{1\/3}x1\/3, is a value that, when raised to the third power (multiplied by itself three times), gives xxx. Mathematically, this can be expressed as:x3=ysuch thaty3=x\\sqrt[3]{x} = y \\quad \\text{such that} \\quad y^3 = x3x\u200b=ysuch thaty3=x<\/p>\n\n\n\n For example, 83=2\\sqrt[3]{8} = 238\u200b=2 because 23=82^3 = 823=8.<\/p>\n\n\n\n To simplify 2161\/3216^{1\/3}2161\/3, we begin by finding the prime factorization of 216. We divide 216 by the smallest prime numbers until we reach a product of primes:<\/p>\n\n\n\n Thus, the prime factorization of 216 is:216=23\u00d733216 = 2^3 \\times 3^3216=23\u00d733<\/p>\n\n\n\n Now, we take the cube root of both sides of the equation 216=23\u00d733216 = 2^3 \\times 3^3216=23\u00d733:2163=23\u00d7333\\sqrt[3]{216} = \\sqrt[3]{2^3 \\times 3^3}3216\u200b=323\u00d733\u200b<\/p>\n\n\n\n Since a33=a\\sqrt[3]{a^3} = a3a3\u200b=a, we can simplify this as:2163=2\u00d73=6\\sqrt[3]{216} = 2 \\times 3 = 63216\u200b=2\u00d73=6<\/p>\n\n\n\n Thus, 2161\/3=6216^{1\/3} = 62161\/3=6.<\/p>\n\n\n\n Taking the cube root is a way to reverse cubing a number. Just as the square root is the reverse of squaring a number, the cube root is the reverse of cubing. This is why simplifying cube roots often involves factoring the number into powers of prime numbers. The cube root of a number is particularly useful in geometry and algebra when dealing with volumes of cubes and cubic equations.<\/p>\n","protected":false},"excerpt":{"rendered":" Simplify.216^1\/3 The Correct Answer and Explanation is: To simplify 2161\/3216^{1\/3}2161\/3, we are asked to find the cube root of 216. This means we need to determine which number, when multiplied by itself three times (cubed), gives 216. Step 1: Understanding Cube Roots The cube root of a number xxx, denoted x1\/3x^{1\/3}x1\/3, is a value that, […]<\/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-162244","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162244","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=162244"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162244\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understanding Cube Roots<\/h3>\n\n\n\n
Step 2: Prime Factorization of 216<\/h3>\n\n\n\n
\n
Step 3: Applying the Cube Root<\/h3>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
Explanation of Cube Roots:<\/h3>\n\n\n\n