{"id":256,"date":"2023-06-21T13:22:49","date_gmt":"2023-06-21T13:22:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-14\/"},"modified":"2023-06-21T13:22:49","modified_gmt":"2023-06-21T13:22:49","slug":"summary-review-14","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-14\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"\n\n<h2>Key Equations<\/h2>\n<table style=\"height: 136px\">\n<tbody>\n<tr style=\"height: 31px\">\n<td style=\"height: 31px\" colspan=\"2\"><strong>Rules of Exponents<\/strong>\nFor nonzero real numbers [latex]a[\/latex] and [latex]b[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Product rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Quotient rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Power rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Zero exponent rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{a}^{0}=1[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Negative rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{a}^{-n}=\\dfrac{1}{{a}^{n}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Power of a product rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{\\left(a\\cdot b\\right)}^{n}={a}^{n}\\cdot {b}^{n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Power of a quotient rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{\\left(\\dfrac{a}{b}\\right)}^{n}=\\dfrac{{a}^{n}}{{b}^{n}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li style=\"list-style-type: none\">\n<ul>\n \t<li>Products of exponential expressions with the same base can be simplified by adding exponents.<\/li>\n \t<li>Quotients of exponential expressions with the same base can be simplified by subtracting exponents.<\/li>\n \t<li>Powers of exponential expressions with the same base can be simplified by multiplying exponents.<\/li>\n \t<li>An expression with exponent zero is defined as 1.<\/li>\n \t<li>An expression with a negative exponent is defined as a reciprocal.<\/li>\n \t<li>The power of a product of factors is the same as the product of the powers of the same factors.<\/li>\n \t<li>The power of a quotient of factors is the same as the quotient of the powers of the same factors.<\/li>\n \t<li>The rules for exponential expressions can be combined to simplify more complicated expressions.<\/li>\n \t<li>Corresponding input and output pairs of a function each represent a point on the graph of the function.<\/li>\n \t<li>Each point contained on the graph of a function satisfies the equation of a function.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n","rendered":"<h2>Key Equations<\/h2>\n<table style=\"height: 136px\">\n<tbody>\n<tr style=\"height: 31px\">\n<td style=\"height: 31px\" colspan=\"2\"><strong>Rules of Exponents<\/strong><br \/>\nFor nonzero real numbers [latex]a[\/latex] and [latex]b[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Product rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Quotient rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Power rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Zero exponent rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{a}^{0}=1[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Negative rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{a}^{-n}=\\dfrac{1}{{a}^{n}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Power of a product rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{\\left(a\\cdot b\\right)}^{n}={a}^{n}\\cdot {b}^{n}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><strong>Power of a quotient rule<\/strong><\/td>\n<td style=\"height: 15px\">[latex]{\\left(\\dfrac{a}{b}\\right)}^{n}=\\dfrac{{a}^{n}}{{b}^{n}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>Products of exponential expressions with the same base can be simplified by adding exponents.<\/li>\n<li>Quotients of exponential expressions with the same base can be simplified by subtracting exponents.<\/li>\n<li>Powers of exponential expressions with the same base can be simplified by multiplying exponents.<\/li>\n<li>An expression with exponent zero is defined as 1.<\/li>\n<li>An expression with a negative exponent is defined as a reciprocal.<\/li>\n<li>The power of a product of factors is the same as the product of the powers of the same factors.<\/li>\n<li>The power of a quotient of factors is the same as the quotient of the powers of the same factors.<\/li>\n<li>The rules for exponential expressions can be combined to simplify more complicated expressions.<\/li>\n<li>Corresponding input and output pairs of a function each represent a point on the graph of the function.<\/li>\n<li>Each point contained on the graph of a function satisfies the equation of a function.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-256\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t 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