{"id":223963,"date":"2025-06-02T14:04:31","date_gmt":"2025-06-02T14:04:31","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223963"},"modified":"2025-06-02T14:04:33","modified_gmt":"2025-06-02T14:04:33","slug":"what-is-the-product-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/what-is-the-product-2\/","title":{"rendered":"What is the product"},"content":{"rendered":"\n

What is the product?\\n
\\n
\\n
\\n
\\n<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

To solve the problem shown in the image, we need to find the product: (3a2b3)(5a3b2)(3a^2b^3)(5a^3b^2)<\/p>\n\n\n\n

\n\n\n\n

Step-by-Step Solution:<\/h3>\n\n\n\n

We are multiplying two monomials: (3a2b3)\u00d7(5a3b2)(3a^2b^3) \\times (5a^3b^2)<\/p>\n\n\n\n

    \n
  1. Multiply the constants (numerical coefficients):<\/strong><\/li>\n<\/ol>\n\n\n\n

    3\u00d75=153 \\times 5 = 15<\/p>\n\n\n\n

      \n
    1. Multiply the powers of aa:<\/strong><\/li>\n<\/ol>\n\n\n\n

      a2\u00d7a3=a2+3=a5a^2 \\times a^3 = a^{2+3} = a^5<\/p>\n\n\n\n

        \n
      1. Multiply the powers of bb:<\/strong><\/li>\n<\/ol>\n\n\n\n

        b3\u00d7b2=b3+2=b5b^3 \\times b^2 = b^{3+2} = b^5<\/p>\n\n\n\n

        \n\n\n\n

        Final Answer:<\/h3>\n\n\n\n

        15a5b515a^5b^5<\/p>\n\n\n\n

        \n\n\n\n

        Explanation<\/h3>\n\n\n\n

        When multiplying polynomials or monomials, you apply the product of powers property<\/strong>, which states that if you are multiplying like bases, you add their exponents<\/strong>. This principle is key in simplifying expressions involving variables with exponents.<\/p>\n\n\n\n

        In the given expression (3a2b3)(5a3b2)(3a^2b^3)(5a^3b^2), we start by addressing each part of the expression systematically.<\/p>\n\n\n\n

        First, the numerical coefficients<\/strong> are multiplied. These are simply regular numbers in front of the variables. So, we multiply 33 and 55, giving us 1515.<\/p>\n\n\n\n

        Next, we look at the variables with exponents. We have two types of variables: aa and bb. For each variable, we apply the product of powers rule. For the aa terms: a2\u00d7a3=a2+3=a5a^2 \\times a^3 = a^{2+3} = a^5. Likewise, for the bb terms: b3\u00d7b2=b3+2=b5b^3 \\times b^2 = b^{3+2} = b^5.<\/p>\n\n\n\n

        Combining all the results, we get: 15a5b515a^5b^5<\/p>\n\n\n\n

        This final expression represents the product of the original two monomials. The key takeaway is that multiplication of monomials involves multiplying coefficients and adding the exponents of like bases<\/strong>. This rule is one of the foundations of algebra and is used repeatedly when simplifying polynomial expressions or solving equations that include variable terms raised to powers.<\/p>\n\n\n\n

        \n\n\n\n

        \u2705 Correct Answer:<\/h3>\n\n\n\n

        D. 15a\u2075b\u2075<\/strong><\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        What is the product?\\n\\n\\n\\n\\n The Correct Answer and Explanation is: To solve the problem shown in the image, we need to find the product: (3a2b3)(5a3b2)(3a^2b^3)(5a^3b^2) Step-by-Step Solution: We are multiplying two monomials: (3a2b3)\u00d7(5a3b2)(3a^2b^3) \\times (5a^3b^2) 3\u00d75=153 \\times 5 = 15 a2\u00d7a3=a2+3=a5a^2 \\times a^3 = a^{2+3} = a^5 b3\u00d7b2=b3+2=b5b^3 \\times b^2 = b^{3+2} = b^5 Final […]<\/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-223963","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223963","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=223963"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223963\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}