{"id":40551,"date":"2025-06-27T18:29:09","date_gmt":"2025-06-27T18:29:09","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=40551"},"modified":"2025-06-27T18:29:10","modified_gmt":"2025-06-27T18:29:10","slug":"evaluate-the-following-expression","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/evaluate-the-following-expression\/","title":{"rendered":"Evaluate the following expression"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"750\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-419.png\" alt=\"\" class=\"wp-image-40555\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-419.png 750w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-419-300x300.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-419-150x150.png 150w\" sizes=\"auto, (max-width: 750px) 100vw, 750px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is:<\/p>\n\n\n\n<p>(14)3=164\\left( \\frac{1}{4} \\right)^3 = \\frac{1}{64}<\/p>\n\n\n\n<p>To evaluate the expression (14)3(\\frac{1}{4})^3, we are asked to raise the fraction 14\\frac{1}{4} to the third power. This means we multiply 14\\frac{1}{4} by itself three times. In mathematical terms:<\/p>\n\n\n\n<p>(14)3=14\u00d714\u00d714\\left( \\frac{1}{4} \\right)^3 = \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4}<\/p>\n\n\n\n<p>The multiplication of fractions follows a straightforward rule. Multiply the numerators together and then multiply the denominators. In this case, all the numerators are 1, and all the denominators are 4:<\/p>\n\n\n\n<p>1\u00d71\u00d714\u00d74\u00d74=164\\frac{1 \\times 1 \\times 1}{4 \\times 4 \\times 4} = \\frac{1}{64}<\/p>\n\n\n\n<p>This result tells us that (14)3\\left(\\frac{1}{4}\\right)^3 is equal to 164\\frac{1}{64}.<\/p>\n\n\n\n<p>This problem offers a great opportunity to reinforce the concept of exponentiation with fractions. Exponentiation is the repeated multiplication of a number by itself. When the base is a fraction, both the numerator and denominator are raised to the given power. Since our base is 14\\frac{1}{4}, we cube the numerator and the denominator individually.<\/p>\n\n\n\n<p>1343=164\\frac{1^3}{4^3} = \\frac{1}{64}<\/p>\n\n\n\n<p>This principle applies generally. For any fraction ab\\frac{a}{b}, raising it to the power nn results in anbn\\frac{a^n}{b^n}.<\/p>\n\n\n\n<p>Understanding this foundational concept is essential for more advanced mathematics. It supports work in algebra, scientific notation, and problem-solving involving scale and ratios. By mastering simple exponentiation with fractions like this, learners build confidence and accuracy that will serve them in more complex expressions.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1273.jpeg\" alt=\"\" class=\"wp-image-40557\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1273.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1273-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1273-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is: (14)3=164\\left( \\frac{1}{4} \\right)^3 = \\frac{1}{64} To evaluate the expression (14)3(\\frac{1}{4})^3, we are asked to raise the fraction 14\\frac{1}{4} to the third power. This means we multiply 14\\frac{1}{4} by itself three times. In mathematical terms: (14)3=14\u00d714\u00d714\\left( \\frac{1}{4} \\right)^3 = \\frac{1}{4} \\times \\frac{1}{4} \\times \\frac{1}{4} The multiplication [&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-40551","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40551","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=40551"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40551\/revisions"}],"predecessor-version":[{"id":40558,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40551\/revisions\/40558"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}