{"id":1459,"date":"2021-07-15T22:07:07","date_gmt":"2021-07-15T22:07:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/?post_type=chapter&p=1459"},"modified":"2021-07-15T22:09:04","modified_gmt":"2021-07-15T22:09:04","slug":"module-11-summary-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/chapter\/module-11-summary-review\/","title":{"raw":"Module 11 Summary Review","rendered":"Module 11 Summary Review"},"content":{"raw":"

Key Equations<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Rules of Exponents<\/strong>\r\nFor nonzero real numbers [latex]a[\/latex] and [latex]b[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]<\/td>\r\n<\/tr>\r\n
Product rule<\/strong><\/td>\r\n[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<\/td>\r\n<\/tr>\r\n
Quotient rule<\/strong><\/td>\r\n[latex]\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}[\/latex]<\/td>\r\n<\/tr>\r\n
Power rule<\/strong><\/td>\r\n[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<\/td>\r\n<\/tr>\r\n
Zero exponent rule<\/strong><\/td>\r\n[latex]{a}^{0}=1[\/latex]<\/td>\r\n<\/tr>\r\n
Negative rule<\/strong><\/td>\r\n[latex]{a}^{-n}=\\dfrac{1}{{a}^{n}}[\/latex]<\/td>\r\n<\/tr>\r\n
Power of a product rule<\/strong><\/td>\r\n[latex]{\\left(a\\cdot b\\right)}^{n}={a}^{n}\\cdot {b}^{n}[\/latex]<\/td>\r\n<\/tr>\r\n
Power of a quotient rule<\/strong><\/td>\r\n[latex]{\\left(\\dfrac{a}{b}\\right)}^{n}=\\dfrac{{a}^{n}}{{b}^{n}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Key Concepts<\/h2>\r\n
    \r\n \t
  • \r\n
      \r\n \t
    • Products of exponential expressions with the same base can be simplified by adding exponents.<\/li>\r\n \t
    • Quotients of exponential expressions with the same base can be simplified by subtracting exponents.<\/li>\r\n \t
    • Powers of exponential expressions with the same base can be simplified by multiplying exponents.<\/li>\r\n \t
    • An expression with exponent zero is defined as 1.<\/li>\r\n \t
    • An expression with a negative exponent is defined as a reciprocal.<\/li>\r\n \t
    • The power of a product of factors is the same as the product of the powers of the same factors.<\/li>\r\n \t
    • The power of a quotient of factors is the same as the quotient of the powers of the same factors.<\/li>\r\n \t
    • The rules for exponential expressions can be combined to simplify more complicated expressions.<\/li>\r\n \t
    • Corresponding input and output pairs of a function each represent a point on the graph of the function.<\/li>\r\n \t
    • Each point contained on the graph of a function satisfies the equation of a function.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n","rendered":"

      Key Equations<\/h2>\n\n\n\n\n\n\n\n\n\n\n
      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
      Product rule<\/strong><\/td>\n[latex]{a}^{m}\\cdot {a}^{n}={a}^{m+n}[\/latex]<\/td>\n<\/tr>\n
      Quotient rule<\/strong><\/td>\n[latex]\\dfrac{{a}^{m}}{{a}^{n}}={a}^{m-n}[\/latex]<\/td>\n<\/tr>\n
      Power rule<\/strong><\/td>\n[latex]{\\left({a}^{m}\\right)}^{n}={a}^{m\\cdot n}[\/latex]<\/td>\n<\/tr>\n
      Zero exponent rule<\/strong><\/td>\n[latex]{a}^{0}=1[\/latex]<\/td>\n<\/tr>\n
      Negative rule<\/strong><\/td>\n[latex]{a}^{-n}=\\dfrac{1}{{a}^{n}}[\/latex]<\/td>\n<\/tr>\n
      Power of a product rule<\/strong><\/td>\n[latex]{\\left(a\\cdot b\\right)}^{n}={a}^{n}\\cdot {b}^{n}[\/latex]<\/td>\n<\/tr>\n
      Power of a quotient rule<\/strong><\/td>\n[latex]{\\left(\\dfrac{a}{b}\\right)}^{n}=\\dfrac{{a}^{n}}{{b}^{n}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Key Concepts<\/h2>\n
        \n
      • \n
          \n
        • Products of exponential expressions with the same base can be simplified by adding exponents.<\/li>\n
        • Quotients of exponential expressions with the same base can be simplified by subtracting exponents.<\/li>\n
        • Powers of exponential expressions with the same base can be simplified by multiplying exponents.<\/li>\n
        • An expression with exponent zero is defined as 1.<\/li>\n
        • An expression with a negative exponent is defined as a reciprocal.<\/li>\n
        • The power of a product of factors is the same as the product of the powers of the same factors.<\/li>\n
        • The power of a quotient of factors is the same as the quotient of the powers of the same factors.<\/li>\n
        • The rules for exponential expressions can be combined to simplify more complicated expressions.<\/li>\n
        • Corresponding input and output pairs of a function each represent a point on the graph of the function.<\/li>\n
        • Each point contained on the graph of a function satisfies the equation of a function.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"author":167848,"menu_order":31,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1459","chapter","type-chapter","status-publish","hentry"],"part":1407,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/1459","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/1459\/revisions"}],"predecessor-version":[{"id":1460,"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/1459\/revisions\/1460"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/parts\/1407"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/1459\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/wp\/v2\/media?parent=1459"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1459"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/wp\/v2\/contributor?post=1459"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/dcccd-collegealgebracorequisite\/wp-json\/wp\/v2\/license?post=1459"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}