{"id":450,"date":"2023-02-22T00:00:46","date_gmt":"2023-02-22T00:00:46","guid":{"rendered":"https:\/\/www.matematikazavsicki.com\/en\/?p=450"},"modified":"2023-02-22T00:00:47","modified_gmt":"2023-02-22T00:00:47","slug":"multiplying-and-dividing-exponents-with-same-base","status":"publish","type":"post","link":"https:\/\/www.matematikazavsicki.com\/en\/multiplying-and-dividing-exponents-with-same-base\/","title":{"rendered":"Multiplying and dividing exponents with same base"},"content":{"rendered":"\n<p>On this page, you can find the rules for multiplying and dividing exponents with the same base, ie equal base. In addition to the rules, below is a solved example for both multiplying and dividing exponents with the same base. More solved examples can be seen in the video, which can also be found below in the text.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplying exponents with the same base<\/h2>\n\n\n\n<p>When multiplying exponents with the same base, the following formula applies:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-multiplying-exponents-with-the-same-base.jpg\" alt=\"Formula for multiplying exponents with the same base\" class=\"wp-image-460\" width=\"250\" height=\"58\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-multiplying-exponents-with-the-same-base.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-multiplying-exponents-with-the-same-base-300x69.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure>\n<\/div>\n\n\n<p>from which it can be seen that when multiplying exponents with the same base! So the base remains unchanged after the multiplication! The final exponent represents the sum of the two different exponents that were given before the multiplication.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Example number 1: To determine the product:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-Exponents-with-the-same-base.jpg\" alt=\"Multiplying Exponents with the same base\" class=\"wp-image-462\" width=\"181\" height=\"72\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-Exponents-with-the-same-base.jpg 362w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-Exponents-with-the-same-base-300x119.jpg 300w\" sizes=\"auto, (max-width: 181px) 100vw, 181px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The basis remains 5, and the degree in the result is obtained as a sum of the exponents 7 and 2. The result of task number 1 is:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/The-result-of-multiplying-exponents-with-the-same-base.jpg\" alt=\"The result of multiplying\" class=\"wp-image-464\" width=\"67\" height=\"72\"\/><\/figure>\n<\/div>\n\n\n<p>If when solving this type of problem, one (two or more) of the exponents is a negative number, then the rules for adding integers apply during the calculation. If the degree is a fraction, the rules for adding fractions apply.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Dividing exponents with the same base<\/h2>\n\n\n\n<p>When dividing exponents with the same base, the following formula applies:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-multiplying-exponents-with-the-same-base-1.jpg\" alt=\"Formula for multiplying exponents with the same base\" class=\"wp-image-465\" width=\"250\" height=\"58\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-multiplying-exponents-with-the-same-base-1.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Formula-for-multiplying-exponents-with-the-same-base-1-300x69.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure>\n<\/div>\n\n\n<p>from which it can be seen that when dividing exponents with the same base, the base remains unchanged after the division, while the final exponent represents the difference from the first and second (in the appropriate order) exponents that were given before the division.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Example number 2: To determine the quotient:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Dividing-Exponents-with-the-same-base.jpg\" alt=\"Dividing Exponents with the same base\" class=\"wp-image-466\" width=\"184\" height=\"72\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Dividing-Exponents-with-the-same-base.jpg 368w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Dividing-Exponents-with-the-same-base-300x117.jpg 300w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Dividing-Exponents-with-the-same-base-365x143.jpg 365w\" sizes=\"auto, (max-width: 184px) 100vw, 184px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The base remains the same 5, and the degree in the result is obtained as the difference between exponents 7 and 2 (7-2). The result of task number 2 is:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/The-result-of-dividing-exponents-with-the-same-base.jpg\" alt=\"The result of dividing\" class=\"wp-image-467\" width=\"61\" height=\"73\"\/><\/figure>\n<\/div>\n\n\n<p>When dividing exponents with the same base, if the exponents are integers, we follow the rules for operating with integers. If exponents are fractions, the rules for adding and subtracting fractions apply.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Video Examples<\/h3>\n\n\n\n<p>Finally, in the video below, you can watch solving several example problems for multiplying and dividing exponents with the same base!<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/youtu.be\/sq7UtXpUdnc\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"634\" height=\"356\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-and-dividing-exponents-with-same-base.jpg\" alt=\"Multiplying and dividing exponents with same base\" class=\"wp-image-457\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-and-dividing-exponents-with-same-base.jpg 634w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-and-dividing-exponents-with-same-base-300x168.jpg 300w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/02\/Multiplying-and-dividing-exponents-with-same-base-624x350.jpg 624w\" sizes=\"auto, (max-width: 634px) 100vw, 634px\" \/><\/a><\/figure>\n<\/div>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<form role=\"search\" method=\"get\" action=\"https:\/\/www.matematikazavsicki.com\/en\/\" class=\"wp-block-search__button-outside wp-block-search__text-button wp-block-search\"    ><label class=\"wp-block-search__label\" for=\"wp-block-search__input-1\" >Enter the mathematical term you want to explore!<\/label><div class=\"wp-block-search__inside-wrapper\" ><input class=\"wp-block-search__input\" id=\"wp-block-search__input-1\" placeholder=\"What do you want to study?\" value=\"\" type=\"search\" name=\"s\" required \/><button aria-label=\"Search\" class=\"wp-block-search__button wp-element-button\" type=\"submit\" >Search<\/button><\/div><\/form>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<p>Follow the information and materials that will be published in the future. Complete connection with the www.matematikazavsicki.com\/en profiles on Facebook, and Youtube using the buttons below.<\/p>\n\n\n\n<div class=\"wp-block-wpzoom-blocks-social-icons is-style-with-canvas-round\" style=\"--wpz-social-icons-block-item-font-size:65px;--wpz-social-icons-block-item-padding-horizontal:6px;--wpz-social-icons-block-item-padding-vertical:6px;--wpz-social-icons-block-item-margin-horizontal:5px;--wpz-social-icons-block-item-margin-vertical:5px;--wpz-social-icons-block-item-border-radius:50px;--wpz-social-icons-block-label-font-size:16px;--wpz-social-icons-block-label-color:#2e3131;--wpz-social-icons-block-label-color-hover:#2e3131;--wpz-social-icons-alignment:center\"><a href=\"https:\/\/www.facebook.com\/mathforallvideo\/\" class=\"social-icon-link\" title=\"Facebook\" style=\"--wpz-social-icons-block-item-color:#1877F2;--wpz-social-icons-block-item-color-hover:#1877F2\"><span class=\"social-icon socicon socicon-facebook\"><\/span><\/a><a href=\"https:\/\/www.youtube.com\/@mathforallvideos\" class=\"social-icon-link\" title=\"Youtube\" style=\"--wpz-social-icons-block-item-color:#e02a20;--wpz-social-icons-block-item-color-hover:#e02a20\"><span class=\"social-icon socicon socicon-youtube\"><\/span><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>On this page, you can find the rules for multiplying and dividing exponents with the same base, ie equal base. In addition to the rules, below is a solved example [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":472,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,5,6,7,11],"tags":[85,81,82,80,84,83],"class_list":["post-450","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10th-grade","category-7th-grade","category-8th-grade","category-9th-grade","category-algebra","tag-base","tag-dividing","tag-exponents","tag-multiplying","tag-same","tag-with"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Multiplying and dividing exponents with same base - Math For All<\/title>\n<meta name=\"description\" content=\"On this page, you can find the rules for multiplying and dividing exponents with the same base, ie equal base.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.matematikazavsicki.com\/en\/multiplying-and-dividing-exponents-with-same-base\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Multiplying and dividing exponents with same base - 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