{"id":19848,"date":"2025-06-13T21:52:06","date_gmt":"2025-06-13T21:52:06","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=19848"},"modified":"2025-06-13T21:52:10","modified_gmt":"2025-06-13T21:52:10","slug":"which-is-equivalent-to-64-superscript-one-fourth","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-is-equivalent-to-64-superscript-one-fourth\/","title":{"rendered":"Which is equivalent to 64 Superscript one-fourth"},"content":{"rendered":"\n<p>Which is equivalent to 64 Superscript one-fourth?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p><strong>64^(1\/4) = 2.828<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>The expression <strong>64^(1\/4)<\/strong> means \u201cthe <strong>fourth root<\/strong> of 64,\u201d or in other words, <strong>what number raised to the power of 4 equals 64<\/strong>?<\/p>\n\n\n\n<p>To understand this, recall how exponents and roots work:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>square root<\/strong> of a number is the number that when squared gives the original number.<\/li>\n\n\n\n<li>The <strong>fourth root<\/strong> is the number that when raised to the power of 4 gives the original number.<\/li>\n<\/ul>\n\n\n\n<p>So: x4=64x^4 = 64<\/p>\n\n\n\n<p>We try small whole numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>14=11^4 = 1<\/li>\n\n\n\n<li>24=162^4 = 16<\/li>\n\n\n\n<li>34=813^4 = 81<\/li>\n<\/ul>\n\n\n\n<p>So clearly, <strong>64 is between 16 and 81<\/strong>, and we now know: 2&lt;641\/4&lt;32 &lt; 64^{1\/4} &lt; 3<\/p>\n\n\n\n<p>To solve this more precisely, convert the expression: 641\/4=(26)1\/4=26\/4=23\/264^{1\/4} = (2^6)^{1\/4} = 2^{6\/4} = 2^{3\/2}<\/p>\n\n\n\n<p>Now simplify: 23\/2=23=82^{3\/2} = \\sqrt{2^3} = \\sqrt{8}<\/p>\n\n\n\n<p>And since: 8=4\u22c52=22\\sqrt{8} = \\sqrt{4 \\cdot 2} = 2\\sqrt{2}<\/p>\n\n\n\n<p>Using decimal approximation:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2\u22481.414\\sqrt{2} \\approx 1.414<\/li>\n\n\n\n<li>2\u22c51.414\u22482.8282 \\cdot 1.414 \\approx 2.828<\/li>\n<\/ul>\n\n\n\n<p>Therefore: 641\/4=23\/2=8\u22482.82864^{1\/4} = 2^{3\/2} = \\sqrt{8} \\approx 2.828<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>641\/4\u22482.828\\boxed{64^{1\/4} \\approx 2.828}<\/p>\n\n\n\n<p>This demonstrates how fractional exponents can be simplified using root and power rules. It is useful in algebra and higher-level math when solving exponential and radical expressions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which is equivalent to 64 Superscript one-fourth? The correct answer and explanation is: Correct Answer: 64^(1\/4) = 2.828 Explanation (300 words): The expression 64^(1\/4) means \u201cthe fourth root of 64,\u201d or in other words, what number raised to the power of 4 equals 64? To understand this, recall how exponents and roots work: So: x4=64x^4 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-19848","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19848","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=19848"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19848\/revisions"}],"predecessor-version":[{"id":19849,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19848\/revisions\/19849"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19848"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19848"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19848"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}