{"id":2682,"date":"2012-09-11T09:00:57","date_gmt":"2012-09-11T16:00:57","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=2682"},"modified":"2020-03-25T17:58:29","modified_gmt":"2020-03-26T00:58:29","slug":"adding-and-subtracting-powers-on-the-gmat","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/","title":{"rendered":"Adding and Subtracting Powers on the GMAT"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Subtract-GMAT.png\" alt=\"Adding and Subtracting Powers GMAT-magoosh\" width=\"1200\" height=\"600\" class=\"aligncenter size-full wp-image-9395\" srcset=\"https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Subtract-GMAT.png 1200w, https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Subtract-GMAT-300x150.png 300w, https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Subtract-GMAT-600x300.png 600w, https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Subtract-GMAT-768x384.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p>First, consider this practice problem:<br \/>\n<a name=\"practiceQuestion1\"><\/a><\/p>\n<div class=\"mox\">\n<ol>\n<li>\\(7^6 + 7^8\\)<\/li>\n<\/ol>\n<p><input name=\"choice-q1\" id=\"Q1A\" type=\"radio\" value=\"A\" \/><label for=\"Q1A\">A. \\(7^{14}\\)<\/label><br \/>\n<input name=\"choice-q1\" id=\"Q1B\" type=\"radio\" value=\"B\" \/><label for=\"Q1B\">B. \\(7^{16}\\)<\/label><br \/>\n<input name=\"choice-q1\" id=\"Q1C\" type=\"radio\" value=\"C\" \/><label for=\"Q1C\">C. \\(7^{48}\\)<\/label><br \/>\n<input name=\"choice-q1\" id=\"Q1D\" type=\"radio\" value=\"D\" \/><label for=\"Q1D\">D. \\(14^{14}\\)<\/label><br \/>\n<input name=\"choice-q1\" id=\"Q1E\" type=\"radio\" value=\"E\" \/><label for=\"Q1E\">E. \\((50)\\times(7^6)\\)<\/label><\/div>\n<p>If this problem makes your head spin, you have found the right blog article!<\/p>\n<h2>Operations with powers<\/h2>\n<p>There are legitimate laws of exponents for multiplying and dividing powers. <\/p>\n<p>Take a look at these examples:<\/p>\n<ul>\n<li>\\(a\\times(b + c) = a\\times b + a\\times c\\)<\/li>\n<p>&nbsp;<\/p>\n<li>\\((a^m) \\times (a^n) = a^{m + n}\\)<\/li>\n<p>&nbsp;<\/p>\n<li>\\( \\frac{a^m}{a^n} = a^{m \u2013 n}\\)<\/li>\n<p>&nbsp;<\/p>\n<li>\\((7^8) \\times (7^6) = 7^{8+6} = 7^{14}\\)<\/li>\n<p>&nbsp;<\/p>\n<li>\\( \\frac{7^8}{7^6} = 7^{8 \u2013 6} = 7^2 = 49\\)<\/li>\n<\/ul>\n<p>Multiplying powers means add the exponents and dividing powers means subtract the exponents.  For more on this, see this post on <a href=\"https:\/\/magoosh.com\/gmat\/exponent-properties-on-the-gmat\/\">exponent properties<\/a>.<\/p>\n<p>Alas!  There is no law of exponents for adding and subtracting powers. \ud83d\ude22 <\/p>\n<p>In other words, \\(a^n\\) plus or minus \\(a^m\\) is not going to equal a-to-the-power-of-anything-in-particular.  <\/p>\n<p>There is no convenient way to combine a sum or difference of powers into a single power expression.<\/p>\n<h2>Distributing and factoring out<\/h2>\n<p>But, all is not lost!  We can avail ourselves of one of the fundamental number properties, the Distributive Law, and its inverse process, &#8220;factoring out.&#8221;<\/p>\n<p>That is a rather remarkable and often underestimated equation.  <\/p>\n<p>First of all, it is a statement of the Distributive Law. Remember \\(a\\times(b + c) = a\\times b + a\\times c\\)?<\/p>\n<blockquote><p>If we start on the left and go to the right, we are <strong>distributing<\/strong> &#8220;a.&#8221;  The reverse process is called <strong>factoring out<\/strong>: if we start on the right side, and go to the left, we are factoring &#8220;a&#8221; out.<\/p><\/blockquote>\n<p>Multiplication distributes over addition and subtraction: we could replace both plus signs with minus signs in that equation and it would still be true.<\/p>\n<p>Written in simple variable form, it probably doesn&#8217;t look all that earth-shattering, but the implications of that equation are so widespread as to boggle the mind.  Addition and subtraction of variables, addition and subtraction of fractions, and all techniques for factoring quadratics are ultimately dependent on this profound fundamental law.<\/p>\n<p>Before discussing the implications for addition and subtraction of powers, I will just make one more point.  In this above equation, &#8220;a&#8221; can be any common factor of the two terms on the right, but in some sense, we &#8220;maximize&#8221; the effect of factoring out when the factor we factor out is the Greatest Common Factor (the GCF).  See <a href=\"https:\/\/magoosh.com\/gmat\/gmat-math-factors\/\">this link<\/a> for a review of how GCF works with numbers.<\/p>\n<h2>Factoring out to add &amp; subtract powers<\/h2>\n<p>Suppose we want to simplify \\(2^{17} &#8211; 2^{13} = ?\\)<\/p>\n<p>Well, since both terms are powers of two, they share several common factors (\\(2^1\\), \\(2^2\\), \\(2^3\\), etc.).  <\/p>\n<p>The GCF of both of these terms is \\(2^{13}\\) itself.  We can express each term as the product of the GCF and something else.<\/p>\n<p>\\(2^{17} = (2^4) \\times (2^{13})\\)<\/p>\n<p>&nbsp;<\/p>\n<p>\\(2^{13} = (1) \\times (2^{13})\\)<\/p>\n<p>Now, we can write the difference of powers as<\/p>\n<p>\\(2^{17} &#8211; 2^{13} = (2^4)\\times (2^{13}) &#8211; (1)\\times (2^{13}) = ?\\)<\/p>\n<p>I realize that, at the moment, it may not be completely obvious that this will ultimately be a step in the direction of <em>simplification<\/em> &#8212; it looks like we made everything gratuitously more complex in the second step!  Trust that things will simplify soon!  Here&#8217;s the Distributive Law equation again, now with subtraction and with left &amp; right switched from above.<\/p>\n<p>\\(a \\times b \u2013 a \\times c = a \\times (b \u2013 c)\\)<\/p>\n<p>Notice that the second step of the power subtraction equation matches perfectly the pattern on the left of this statement of the Distributive Law: \\(a = 2^{13}\\), \\(b = 2^4\\) and \\(c = 1\\).  Following this pattern, we see this turns into:<\/p>\n<p>\\(2^{17}  &#8211; 2^{13} = (2^4)\\times (2^{13}) &#8211; (1)\\times (2^{13}) = (2^{13})\\times [(2^4) &#8211; 1]\\)<\/p>\n<p>Now, it&#8217;s germane to point out: we should be able to simplify \\(2^4\\).<\/p>\n<p>\\(2^1 = 1\\)<br \/>\n&nbsp;<br \/>\n\\(2^2 = 4\\)<br \/>\n&nbsp;<br \/>\n\\(2^3 = 8\\)<br \/>\n&nbsp;<br \/>\n\\(2^4 = 16\\)<\/p>\n<p>That, in turn, allows us to simplify the piece in the brackets in the last expression:<\/p>\n<p>\\(2^{17} &#8211; 2^{13} = (2^4)\\times (2^{13}) &#8211; (1)\\times (2^{13}) = (2^{13})\\times [(2^4) &#8211; 1]\\)<br \/>\n&nbsp;<br \/>\n\\(= (2^{13})\\times [16 &#8211; 1] = (2^{13})\\times (15) \\)<\/p>\n<p>Voila!  That final expression, fifteen times two to the thirteen, is the simplification of the difference of two powers.<\/p>\n<p>This process would be particularly important if, for example, you were asked to simplify something like:<\/p>\n<p>\\(\\frac{[2^{17} &#8211; 2^{13}]}{20}\\)<\/p>\n<p>We can&#8217;t cancel from either term in the numerator as long as we have addition or subtraction in the numerator, but once we simplify the numerator so that it&#8217;s all multiplication, we can cancel.  You should verify for yourself that:<\/p>\n<p>\\(\\frac{[2^{17} &#8211; 2^{13}]}{20} = (3)\\times (2^{11})\\)<\/p>\n<p>A remarkable simplification!<\/p>\n<h2>Further Practice<\/h2>\n<p>Now that you have seen that, take another look at the practice question from above, before reading the answer and explanation below.<\/p>\n<p>Practice question #1<\/p>\n<p>Remember the first practice question you encountered before this article began? <\/p>\n<div class=\"mox\">\n<ol>\n<li>\\(7^6 + 7^8\\)<\/li>\n<\/ol>\n<p><input name=\"choice-q3\" type=\"radio\" id=\"Q3A\" value=\"A\" \/><label for=\"Q3A\">A. \\(7^{14}\\)<\/label><br \/>\n<input name=\"choice-q3\" type=\"radio\" id=\"Q3B\" value=\"B\" \/><label for=\"Q3B\">B. \\(7^{16}\\)<\/label><br \/>\n<input name=\"choice-q3\" type=\"radio\" id=\"Q3C\" value=\"C\" \/><label for=\"Q3C\">C. \\(7^{48}\\)<\/label><br \/>\n<input name=\"choice-q3\" type=\"radio\" id=\"Q3D\" value=\"D\" \/><label for=\"Q3D\">D. \\(14^{14}\\)<\/label><br \/>\n<input name=\"choice-q3\" type=\"radio\" id=\"Q3E\" value=\"E\" \/><label for=\"Q3E\">E. \\((50)\\times(7^6)\\)<\/label><\/p>\n<details>\n<summary><span style=\"color:#005bc2\">Click here for the answer and explanation to practice question #1<\/span><\/summary>\n<p>The GCF of  \\(7^6 \\)and \\(7^8\\) is \\(7^6\\).<\/p>\n<p>\\(7^6 = (1)\\times (7^6)\\)<br \/>\n&nbsp;<br \/>\n\\(7^8 = (7^2)\\times (7^6)\\)<\/p>\n<p>Therefore<\/p>\n<p>\\(7^6 + 7^8 = (1)\\times (7^6) + (7^2)\\times (7^6) = [1 + 7^2]\\times (7^6) \\)<br \/>\n&nbsp;<br \/>\n\\(= [1 + 49]\\times (7^6)\\)&nbsp;<br \/>\n\\(= (50)\\times (7^6)\\)<\/p>\n<p>Answer = <strong>E<\/strong><\/details>\n<\/div>\n<p>Did your answer change after you read this post? Let us know in the comments below.<\/p>\n<p>Practice question #2<\/p>\n<div class=\"mox\">\n<ol start=\"2\">\n<li>if \\(2^{2n} + 2^{2n} + 2^{2n} + 2^{2n} = 4^{24}\\), then n<\/li>\n<\/ol>\n<p><input name=\"choice-q2\" type=\"radio\" id=\"Q2A\" value=\"A\" \/><label for=\"Q2A\">A. 3<\/label><br \/>\n<input name=\"choice-q2\" type=\"radio\" id=\"Q2B\" value=\"B\" \/><label for=\"Q2B\">B. 6<\/label><br \/>\n<input name=\"choice-q2\" type=\"radio\" id=\"Q2C\" value=\"C\" \/><label for=\"Q2C\">C. 12<\/label><br \/>\n<input name=\"choice-q2\" type=\"radio\" id=\"Q2D\" value=\"D\" \/><label for=\"Q2D\">D. 23<\/label><br \/>\n<input name=\"choice-q2\" type=\"radio\" id=\"Q2E\" value=\"E\" \/><label for=\"Q2E\">E. 24<\/label><\/p>\n<p>&#x25B6; <a href=\"https:\/\/gmat.magoosh.com\/questions\/709\/a\/343989164?utm_source=gmatblog&#038;utm_medium=blog&#038;utm_campaign=exponents&#038;utm_term=inline\" target=\"_blank\" rel=\"noopener noreferrer\"> Click here for the answer and explanation to practice question #2<\/div>\n","protected":false},"excerpt":{"rendered":"<p>First, consider this practice problem: A. B. C. D. E. If this problem makes your head spin, you have found the right blog article! Operations with powers There are legitimate laws of exponents for multiplying and dividing powers. Take a look at these examples: &nbsp; &nbsp; &nbsp; &nbsp; Multiplying powers means add the exponents and [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":9397,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[160],"tags":[],"ppma_author":[13209],"class_list":["post-2682","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arithmetic"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Adding and Subtracting Powers on the GMAT - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\n<meta name=\"description\" content=\"There&#039;s no easy method for solving questions that involve adding and subtracting exponents but learn some strategies here to help you on test day!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Adding and Subtracting Powers on the GMAT\" \/>\n<meta property=\"og:description\" content=\"There&#039;s no easy method for solving questions that involve adding and subtracting exponents but learn some strategies here to help you on test day!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GMAT\u00ae Exam\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshGMAT\/\" \/>\n<meta property=\"article:published_time\" content=\"2012-09-11T16:00:57+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-03-26T00:58:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Sub-GMAT-FT.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"1200\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mike M\u1d9cGarry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"Adding and Subtracting Powers on the GMAT\",\"datePublished\":\"2012-09-11T16:00:57+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\"},\"wordCount\":920,\"commentCount\":21,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Arithmetic\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\",\"name\":\"Adding and Subtracting Powers on the GMAT - Magoosh Blog \u2014 GMAT\u00ae Exam\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\"},\"datePublished\":\"2012-09-11T16:00:57+00:00\",\"description\":\"There's no easy method for solving questions that involve adding and subtracting exponents but learn some strategies here to help you on test day!\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/gmat\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Adding and Subtracting Powers on the GMAT\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#website\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"name\":\"Magoosh Blog \u2014 GMAT\u00ae Exam\",\"description\":\"Everything you need to know about the GMAT\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/gmat\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gmat\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/MagooshGMAT\/\",\"https:\/\/twitter.com\/MagooshGMAT\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\",\"name\":\"Mike M\u1d9cGarry\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/15a1e36ef1c2c3940179212433de141a\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g\",\"caption\":\"Mike M\u1d9cGarry\"},\"description\":\"Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.\",\"sameAs\":[\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\"],\"award\":[\"Magna cum laude from Harvard\"],\"knowsAbout\":[\"GMAT\"],\"knowsLanguage\":[\"English\"],\"jobTitle\":\"Content Creator\",\"worksFor\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Adding and Subtracting Powers on the GMAT - Magoosh Blog \u2014 GMAT\u00ae Exam","description":"There's no easy method for solving questions that involve adding and subtracting exponents but learn some strategies here to help you on test day!","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/","og_locale":"en_US","og_type":"article","og_title":"Adding and Subtracting Powers on the GMAT","og_description":"There's no easy method for solving questions that involve adding and subtracting exponents but learn some strategies here to help you on test day!","og_url":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/","og_site_name":"Magoosh Blog \u2014 GMAT\u00ae Exam","article_publisher":"https:\/\/www.facebook.com\/MagooshGMAT\/","article_published_time":"2012-09-11T16:00:57+00:00","article_modified_time":"2020-03-26T00:58:29+00:00","og_image":[{"width":1200,"height":1200,"url":"https:\/\/magoosh.com\/gmat\/files\/2012\/09\/Add-Sub-GMAT-FT.png","type":"image\/png"}],"author":"Mike M\u1d9cGarry","twitter_card":"summary_large_image","twitter_creator":"@MagooshGMAT","twitter_site":"@MagooshGMAT","twitter_misc":{"Written by":"Mike M\u1d9cGarry","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/#article","isPartOf":{"@id":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/"},"author":{"name":"Mike M\u1d9cGarry","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b"},"headline":"Adding and Subtracting Powers on the GMAT","datePublished":"2012-09-11T16:00:57+00:00","mainEntityOfPage":{"@id":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/"},"wordCount":920,"commentCount":21,"publisher":{"@id":"https:\/\/magoosh.com\/gmat\/#organization"},"articleSection":["GMAT Arithmetic"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/","url":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/","name":"Adding and Subtracting Powers on the GMAT - Magoosh Blog \u2014 GMAT\u00ae Exam","isPartOf":{"@id":"https:\/\/magoosh.com\/gmat\/#website"},"datePublished":"2012-09-11T16:00:57+00:00","description":"There's no easy method for solving questions that involve adding and subtracting exponents but learn some strategies here to help you on test day!","breadcrumb":{"@id":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/magoosh.com\/gmat\/adding-and-subtracting-powers-on-the-gmat\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/magoosh.com\/gmat\/"},{"@type":"ListItem","position":2,"name":"Adding and Subtracting Powers on the GMAT"}]},{"@type":"WebSite","@id":"https:\/\/magoosh.com\/gmat\/#website","url":"https:\/\/magoosh.com\/gmat\/","name":"Magoosh Blog \u2014 GMAT\u00ae Exam","description":"Everything you need to know about the GMAT","publisher":{"@id":"https:\/\/magoosh.com\/gmat\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/magoosh.com\/gmat\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/magoosh.com\/gmat\/#organization","name":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/","url":"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png","contentUrl":"https:\/\/magoosh.com\/gmat\/files\/2019\/04\/Magoosh-logo-purple-60h.png","width":265,"height":60,"caption":"Magoosh"},"image":{"@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/MagooshGMAT\/","https:\/\/twitter.com\/MagooshGMAT"]},{"@type":"Person","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b","name":"Mike M\u1d9cGarry","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/image\/15a1e36ef1c2c3940179212433de141a","url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","caption":"Mike M\u1d9cGarry"},"description":"Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's Youtube video explanations.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as \"member of the month\" for over two years at <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike's <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/2682","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=2682"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/2682\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media\/9397"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=2682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=2682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=2682"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=2682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}