{"id":91,"date":"2017-08-23T07:47:00","date_gmt":"2017-08-23T07:47:00","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/mathematics\/?page_id=91"},"modified":"2017-08-30T05:42:42","modified_gmt":"2017-08-30T05:42:42","slug":"laws-of-integer-exponents","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/mathematics\/laws-of-integer-exponents\/","title":{"rendered":"Laws of Integer Exponents"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/conic-sections\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/algebra-functions-ii\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/laws-of-fractional-exponents\">Next Lesson \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">Laws of Integer Exponents<\/h1>\n<h4>Objective<\/h4>\n<p>In this lesson, you will study the properties of multiplication, division, addition, and subtraction for integer\u00a0exponents. You will also study additional laws that come into play when solving expressions with a product of terms\u00a0raised to a power, and the power of a power.<\/p>\n<h4>Previously Covered:<\/h4>\n<ul>\n<li><em><strong>Conic sections\u00a0<\/strong><\/em>are shapes created by a geometric plane intersecting a single or\u00a0double cone.<\/li>\n<li>Three types of conic sections are:\n<ul>\n<li><strong>circles, <\/strong><\/li>\n<li><strong>parabolas,<\/strong> and<\/li>\n<li><strong>ellipses. <\/strong><\/li>\n<\/ul>\n<\/li>\n<li>There exists a <strong><em>standard form<\/em><\/strong> for\u00a0each type of conic. This equation can be used to graph the\u00a0conics.<\/li>\n<\/ul>\n<section>\n<h3>What are operations can be performed on integer exponents?<\/h3>\n<h4>Addition and Subtraction<\/h4>\n<p>Only like terms can be added or subtracted. When combining like\u00a0terms through either addition or subtraction, the coefficients in\u00a0front of the variable will be combined, while the exponent will\u00a0remain the same.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image003.gif\" width=\"50\" height=\"14\" name=\"graphics3\" align=\"BOTTOM\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image006.gif\" width=\"19\" height=\"14\" name=\"graphics4\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image009.gif\" width=\"12\" height=\"14\" name=\"graphics5\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image012.gif\" width=\"19\" height=\"14\" name=\"graphics6\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image015.gif\" width=\"14\" height=\"11\" name=\"graphics7\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is A. First, we must decide if the terms\u00a0being added are like terms. Because each term has the same\u00a0variable, with the same exponent, we know that these are like\u00a0terms. We then add the coefficients of each term, resulting in\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image018.gif\" width=\"19\" height=\"14\" name=\"graphics8\" align=\"BOTTOM\" border=\"0\" \/>.<\/p>\n<\/div>\n<\/section>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image021.gif\" width=\"124\" height=\"14\" name=\"graphics9\" align=\"BOTTOM\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image024.gif\" width=\"68\" height=\"14\" name=\"graphics10\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image027.gif\" width=\"68\" height=\"14\" name=\"graphics11\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image030.gif\" width=\"58\" height=\"14\" name=\"graphics12\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image033.gif\" width=\"58\" height=\"14\" name=\"graphics13\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is D.\u00a0Again, we have to determine if we have like terms, and if so, we\u00a0must combine them. Any remaining terms stay separate. Since all\u00a0of the terms have <em>x\u00a0<\/em>as the variable, we must look for terms with equivalent\u00a0exponents. There are three like terms and one separate term.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image036.gif\" width=\"135\" height=\"14\" name=\"graphics14\" align=\"BOTTOM\" border=\"0\" \/>,<br \/>\nand the separate term is\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image039.gif\" width=\"19\" height=\"14\" name=\"graphics15\" align=\"BOTTOM\" border=\"0\" \/>.<br \/>\nSimplified, this is\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image042.gif\" width=\"58\" height=\"14\" name=\"graphics16\" align=\"BOTTOM\" border=\"0\" \/>.<\/p>\n<\/div>\n<\/section>\n<h4>Multiplication<\/h4>\n<p>The <abbr title=\" Let b, x, and y be positive numbers with b \u2260 1. log&lt;sub&gt;b&lt;\/sub&gt;xy = log&lt;sub&gt;b&lt;\/sub&gt;x + log&lt;sub&gt;b&lt;\/sub&gt;y\">product property<\/abbr> states that\u00a0when multiplying two or more terms with the same base, you should\u00a0add the exponents. For example,\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image045.gif\" width=\"114\" height=\"17\" name=\"graphics17\" align=\"ABSMIDDLE\" border=\"0\" \/>.\u00a0This is read, \u201c<em>y\u00a0to the second power multiplied by y to the third power is equal to\u00a0y to the fifth power<\/em>.\u201d<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct multiplication of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image048.gif\" width=\"34\" height=\"14\" name=\"graphics18\" align=\"BOTTOM\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image051.gif\" width=\"12\" height=\"14\" name=\"graphics19\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image054.gif\" width=\"16\" height=\"14\" name=\"graphics20\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image057.gif\" width=\"12\" height=\"14\" name=\"graphics21\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image060.gif\" width=\"12\" height=\"14\" name=\"graphics22\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is A.\u00a0In this problem, both terms have the same base, <em>x<\/em>.\u00a0Therefore, we add the exponents.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image063.gif\" width=\"107\" height=\"14\" name=\"graphics23\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>The <em><strong>power of a power<\/strong><\/em> property is\u00a0used when an exponent is raised to a power. It states that when\u00a0an exponent is raised to a power, we must multiply the exponent\u00a0and the power. For example,\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image066.gif\" width=\"61\" height=\"28\" name=\"graphics24\" align=\"ABSMIDDLE\" border=\"0\" \/>.\u00a0This is read, \u201c<em>x\u00a0to the third power raised to the second power is equal to x to\u00a0the sixth power<\/em>.\u201d<\/p>\n<\/div>\n<\/section>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image069.gif\" width=\"31\" height=\"28\" name=\"graphics25\" align=\"ABSMIDDLE\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image072.gif\" width=\"18\" height=\"17\" name=\"graphics26\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image075.gif\" width=\"14\" height=\"17\" name=\"graphics27\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image078.gif\" width=\"14\" height=\"17\" name=\"graphics28\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image081.gif\" width=\"14\" height=\"17\" name=\"graphics29\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is A. The term\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image084.gif\" width=\"14\" height=\"17\" name=\"graphics30\" align=\"ABSMIDDLE\" border=\"0\" \/>\u00a0is raised to the power of 3.Therefore, 3 is multiplied by 4 to\u00a0get the final exponent, 12.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image087.gif\" width=\"106\" height=\"28\" name=\"graphics31\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<\/div>\n<\/section>\n<p>When a product of terms is raised to a power, the power is\u00a0distributed to each term. For example, to simplify\u00a0<img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image090.gif\" name=\"graphics32\" \/>\u00a0the 2 is distributed to each term inside the parenthesis:\u00a0<img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image093.gif\" name=\"graphics33\" \/>.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image096.gif\" width=\"50\" height=\"28\" name=\"graphics34\" align=\"ABSMIDDLE\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image099.gif\" width=\"43\" height=\"17\" name=\"graphics35\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image102.gif\" width=\"34\" height=\"17\" name=\"graphics36\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image105.gif\" width=\"43\" height=\"17\" name=\"graphics37\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image108.gif\" width=\"43\" height=\"17\" name=\"graphics38\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is C. The term\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image111.gif\" width=\"34\" height=\"17\" name=\"graphics39\" align=\"ABSMIDDLE\" border=\"0\" \/>\u00a0is a product of the terms 3,\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image114.gif\" width=\"12\" height=\"14\" name=\"graphics40\" align=\"BOTTOM\" border=\"0\" \/>,\u00a0and\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image117.gif\" width=\"14\" height=\"17\" name=\"graphics41\" align=\"ABSMIDDLE\" border=\"0\" \/>.\u00a0The exponent 3 outside of the parentheses raises each individual\u00a0term the power of 3. Therefore, 3 is distributed.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p2_clip_image120.gif\" width=\"191\" height=\"28\" name=\"graphics42\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<\/div>\n<\/section>\n<h3>Division<\/h3>\n<p>When dividing powers that have the same base, we find the\u00a0difference of the exponents. For example,<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image003.gif\" width=\"176\" height=\"43\" name=\"graphics3\" align=\"BOTTOM\" border=\"0\" \/>.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image006.gif\" width=\"31\" height=\"43\" name=\"graphics4\" align=\"ABSMIDDLE\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image009.gif\" width=\"12\" height=\"14\" name=\"graphics5\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image012.gif\" width=\"12\" height=\"14\" name=\"graphics6\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image015.gif\" width=\"12\" height=\"14\" name=\"graphics7\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image018.gif\" width=\"12\" height=\"14\" name=\"graphics8\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is B. The numerator and denominator have\u00a0the same base, therefore we find the difference of the exponents.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image021.gif\" width=\"105\" height=\"43\" name=\"graphics9\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<\/div>\n<\/section>\n<p>When the quotient is raised to a power, the power is\u00a0distributed to each term in the numerator and denominator. For\u00a0example,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image024.gif\" width=\"116\" height=\"46\" name=\"graphics10\" align=\"ABSMIDDLE\" border=\"0\" \/>.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image027.gif\" width=\"58\" height=\"45\" name=\"graphics11\" align=\"ABSMIDDLE\" border=\"0\" \/>?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image030.gif\" width=\"26\" height=\"17\" name=\"graphics12\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image033.gif\" width=\"26\" height=\"17\" name=\"graphics13\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image036.gif\" width=\"34\" height=\"17\" name=\"graphics14\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image039.gif\" width=\"35\" height=\"17\" name=\"graphics15\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is A. The power of 4 is distributed to each\u00a0term in the numerator.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image042.gif\" width=\"140\" height=\"50\" name=\"graphics16\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>Then the quotient property can be used, and we can find the\u00a0difference of exponents with the same bases.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image045.gif\" width=\"254\" height=\"50\" name=\"graphics17\" align=\"BOTTOM\" border=\"0\" \/>.<\/p>\n<\/div>\n<\/section>\n<h4>Negative Exponents<\/h4>\n<p>For negative exponents,\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image048.gif\" width=\"130\" height=\"34\" name=\"graphics18\" align=\"ABSMIDDLE\" border=\"0\" \/>.<\/p>\n<h4>Zero Exponents<\/h4>\n<p>The <em><strong>zero property<\/strong><\/em> of exponents states\u00a0that any number or variable raised to the power of zero is equal\u00a0to one. This can be written\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image051.gif\" width=\"36\" height=\"14\" name=\"graphics19\" align=\"BOTTOM\" border=\"0\" \/>,\u00a0and\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image054.gif\" width=\"60\" height=\"25\" name=\"graphics20\" align=\"ABSMIDDLE\" border=\"0\" \/>.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<div>\n<p>Which choice shows the correct simplification of\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image057.gif\" width=\"35\" height=\"40\" name=\"graphics21\" align=\"ABSMIDDLE\" border=\"0\" \/>\u00a0with positive exponents?<\/p>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image060.gif\" width=\"16\" height=\"37\" name=\"graphics22\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image063.gif\" width=\"27\" height=\"17\" name=\"graphics23\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image066.gif\" width=\"16\" height=\"40\" name=\"graphics24\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image069.gif\" width=\"22\" height=\"40\" name=\"graphics25\" align=\"BOTTOM\" border=\"0\" \/><\/li>\n<\/ol>\n<\/div>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<div class=\"q-reveal\">\n<p>The correct choice is A. In this example, we can make use of\u00a0the quotient property, and the rules for negative and zero\u00a0exponents.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image072.gif\" width=\"161\" height=\"87\" name=\"graphics26\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<p>Finally, we can use the negative exponent property to write\u00a0the equation with positive exponents.<\/p>\n<p align=\"CENTER\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/math\/3\/images\/s7_p3_clip_image075.gif\" width=\"66\" height=\"37\" name=\"graphics27\" align=\"BOTTOM\" border=\"0\" \/><\/p>\n<\/div>\n<\/section>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<div class=\"advance\"><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/conic-sections\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/algebra-functions-ii\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/mathematics\/laws-of-fractional-exponents\">Next Lesson \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Laws of Integer Exponents Objective In this lesson, you will study the properties of multiplication, division, addition, and subtraction for integer\u00a0exponents. You will also study additional laws that come into play when solving expressions with a product of terms\u00a0raised to a power, and the power of a power. Previously [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-91","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/91","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/comments?post=91"}],"version-history":[{"count":9,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/91\/revisions"}],"predecessor-version":[{"id":464,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/91\/revisions\/464"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/media?parent=91"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}