{"id":25542,"date":"2025-06-19T03:44:49","date_gmt":"2025-06-19T03:44:49","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25542"},"modified":"2025-06-19T03:44:51","modified_gmt":"2025-06-19T03:44:51","slug":"simplify-the-following-by-factorization-and-express-in-exponential-form","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/simplify-the-following-by-factorization-and-express-in-exponential-form\/","title":{"rendered":"Simplify the following by factorization and express in exponential form"},"content":{"rendered":"\n<p>Simplify the following by factorization and express in exponential form: 1. 135 multiplied by 375. Hi friends, can you please provide the answer? Thanks.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-light-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To simplify <strong>135 \u00d7 375<\/strong> by factorization and express the result in <strong>exponential form<\/strong>, we begin with prime factorization of both numbers:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Prime Factorization<\/strong><\/h3>\n\n\n\n<p><strong>135<\/strong><br>= 5 \u00d7 27<br>= 5 \u00d7 3 \u00d7 9<br>= 5 \u00d7 3 \u00d7 3 \u00d7 3<br>= <strong>3\u00b3 \u00d7 5<\/strong><\/p>\n\n\n\n<p><strong>375<\/strong><br>= 5 \u00d7 75<br>= 5 \u00d7 5 \u00d7 15<br>= 5 \u00d7 5 \u00d7 5 \u00d7 3<br>= <strong>3 \u00d7 5\u00b3<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Multiply using Exponents<\/strong><\/h3>\n\n\n\n<p>Now multiply:<br><strong>135 \u00d7 375<\/strong><br>= (3\u00b3 \u00d7 5) \u00d7 (3 \u00d7 5\u00b3)<\/p>\n\n\n\n<p>Use exponent rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply like bases by adding exponents:<br><strong>3\u00b3 \u00d7 3\u00b9 = 3\u2074<\/strong><br><strong>5\u00b9 \u00d7 5\u00b3 = 5\u2074<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So,<br><strong>135 \u00d7 375 = 3\u2074 \u00d7 5\u2074<\/strong><\/p>\n\n\n\n<p>This is the <strong>simplified exponential form<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Final Answer<\/strong><\/h3>\n\n\n\n<p>\u2705 <strong>Answer: 3\u2074 \u00d7 5\u2074<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>To simplify the product of 135 and 375 by factorization and express the result in exponential form, we first break each number into its prime factors. Prime factorization is the process of expressing a number as a product of its prime numbers. For example, 135 can be written as 3 \u00d7 3 \u00d7 3 \u00d7 5, which gives 3 raised to the power of 3 and 5 to the power of 1. In exponential form, we write this as 3\u00b3 \u00d7 5.<\/p>\n\n\n\n<p>Similarly, 375 can be factorized as 3 \u00d7 5 \u00d7 5 \u00d7 5, which equals 3 \u00d7 5\u00b3.<\/p>\n\n\n\n<p>Next, we apply the rules of exponents. When multiplying powers with the same base, we add the exponents. That means 3\u00b3 \u00d7 3 = 3\u2074, and 5 \u00d7 5\u00b3 = 5\u2074. So the product becomes 3\u2074 \u00d7 5\u2074.<\/p>\n\n\n\n<p>This method not only simplifies the multiplication but also shows the structure of the number clearly. Exponential form is useful because it makes it easy to work with large numbers, especially in algebra and higher mathematics. Instead of multiplying the numbers directly to get 50,625 (which is the actual product), we express the number as a product of its prime factors raised to powers.<\/p>\n\n\n\n<p>Therefore, the final answer in exponential form is <strong>3\u2074 \u00d7 5\u2074<\/strong>.<\/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-banner8-51.jpeg\" alt=\"\" class=\"wp-image-25543\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-51.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-51-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-51-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Simplify the following by factorization and express in exponential form: 1. 135 multiplied by 375. Hi friends, can you please provide the answer? Thanks. The Correct Answer and Explanation is: To simplify 135 \u00d7 375 by factorization and express the result in exponential form, we begin with prime factorization of both numbers: Step 1: Prime [&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-25542","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25542","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=25542"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25542\/revisions"}],"predecessor-version":[{"id":25544,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25542\/revisions\/25544"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}