{"id":1964,"date":"2021-12-02T19:40:13","date_gmt":"2021-12-03T00:40:13","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-6\/"},"modified":"2023-09-01T14:41:16","modified_gmt":"2023-09-01T18:41:16","slug":"answer-key-9-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-6\/","title":{"raw":"Answer Key 9.6","rendered":"Answer Key 9.6"},"content":{"raw":"
    \r\n \t
  1. [latex]\\sqrt[5]{m^3}[\/latex]<\/li>\r\n \t
  2. [latex]\\dfrac{1}{\\sqrt[4]{(10r)^3}}[\/latex]<\/li>\r\n \t
  3. [latex]\\sqrt{(7x)^3}[\/latex]<\/li>\r\n \t
  4. [latex]\\dfrac{1}{\\sqrt[3]{(6b)^4}}[\/latex]<\/li>\r\n \t
  5. [latex]\\dfrac{1}{\\sqrt{(2x+3)^3}}[\/latex]<\/li>\r\n \t
  6. [latex]\\sqrt[4]{(x-3y)^3}[\/latex]<\/li>\r\n \t
  7. [latex]5^{\\frac{1}{3}}[\/latex]<\/li>\r\n \t
  8. [latex]2^{\\frac{3}{5}}[\/latex]<\/li>\r\n \t
  9. [latex](ab^5)^{\\frac{1}{3}}[\/latex] or [latex]a^{\\frac{1}{3}}b^{\\frac{5}{3}}[\/latex]<\/li>\r\n \t
  10. [latex]x^{\\frac{3}{5}}[\/latex]<\/li>\r\n \t
  11. [latex](a+5)^{\\frac{2}{3}}[\/latex]<\/li>\r\n \t
  12. [latex](a-2)^{\\frac{3}{5}}[\/latex]<\/li>\r\n \t
  13. [latex]8^{\\frac{2}{3}}\\Rightarrow (2^3)^{\\frac{2}{3}}\\Rightarrow 2^2\\text{ or }4[\/latex]<\/li>\r\n \t
  14. [latex]16^{\\frac{1}{4}}\\Rightarrow (2^4)^{\\frac{1}{4}}\\Rightarrow 2[\/latex]<\/li>\r\n \t
  15. [latex]\\sqrt[3]{4^6}\\Rightarrow (2^2)^{\\frac{6}{3}}\\Rightarrow 2^4\\text{ or }16[\/latex]<\/li>\r\n \t
  16. [latex]\\sqrt[5]{32^2}\\Rightarrow (2^5)^{\\frac{2}{5}}\\Rightarrow 2^2\\text{ or }4[\/latex]<\/li>\r\n \t
  17. [latex]x^2y^{\\frac{1}{3}+\\frac{2}{3}}\\Rightarrow x^2y[\/latex]<\/li>\r\n \t
  18. [latex]4v^{\\frac{2}{3}-1}\\Rightarrow 4v^{-\\frac{1}{3}}\\text{ or }\\dfrac{4}{v^{\\frac{1}{3}}}[\/latex]<\/li>\r\n \t
  19. [latex]{a}^{-\\frac{1}{2}}{b}^{-\\frac{1}{2}}\\Rightarrow \\dfrac{1}{{a}^{\\frac{1}{2}}{b}^{\\frac{1}{2}}}[\/latex]<\/li>\r\n \t
  20. 1<\/li>\r\n<\/ol>\r\n
      \r\n \t
    1. [latex]\\dfrac{\\cancel{a^2}\\cancel{b^0}1}{3\\cancel{a^4}a^2}\\Rightarrow \\dfrac{1}{3a^2}[\/latex]<\/li>\r\n \t
    2. [latex]\\dfrac{\\cancel{2}x^{\\frac{1}{2}}y^{\\frac{1}{3}}}{\\cancel{2}x^{\\frac{4}{3}}y^{\\frac{7}{4}}} \\Rightarrow x^{\\frac{1}{2}-\\frac{4}{3}}y^{\\frac{1}{3}-\\frac{7}{4}}\\Rightarrow x^{-\\frac{5}{6}}y^{-\\frac{17}{12}}\\Rightarrow \\dfrac{1}{x^{\\frac{5}{6}}y^{\\frac{17}{12}}}[\/latex]<\/li>\r\n \t
    3. [latex]\\dfrac{a^{\\frac{3}{4}}\\cancel{b^{-1}}b^{\\frac{7}{4}}}{3\\cancel{b^{-1}}}\\Rightarrow \\dfrac{a^{\\frac{3}{4}}b^{\\frac{7}{4}}}{3}[\/latex]<\/li>\r\n \t
    4. [latex]2x^{-2+\\frac{5}{4}-1}y^{\\frac{5}{3}+\\frac{5}{3}-\\frac{1}{2}} \\Rightarrow 2x^{-\\frac{7}{4}}y^{\\frac{17}{6}}\\Rightarrow \\dfrac{2y^{\\frac{17}{6}}}{x^{\\frac{7}{4}}}[\/latex]<\/li>\r\n \t
    5. [latex]\\dfrac{3}{2}y^{-\\frac{5}{4}- -1 - -\\frac{1}{3}} \\Rightarrow \\dfrac{3}{2}y^{\\frac{1}{12}}[\/latex]<\/li>\r\n \t
    6. [latex]\\dfrac{ab^{\\frac{1}{3}}\\cancel{2}b^{-\\frac{5}{4}}}{\\cancel{4}2a^{-\\frac{1}{2}}b^{-\\frac{2}{3}}} \\Rightarrow \\dfrac{1}{2}a^{1- -\\frac{1}{2}}b^{\\frac{1}{3}-\\frac{5}{4}- -\\frac{2}{3}} \\Rightarrow \\dfrac{1}{2}a^{\\frac{3}{2}}b^{-\\frac{1}{4}}\\Rightarrow \\dfrac{a^{\\frac{3}{2}}}{2b^{\\frac{1}{4}}}[\/latex]<\/li>\r\n<\/ol>","rendered":"
        \n
      1. [latex]\\sqrt[5]{m^3}[\/latex]<\/li>\n
      2. [latex]\\dfrac{1}{\\sqrt[4]{(10r)^3}}[\/latex]<\/li>\n
      3. [latex]\\sqrt{(7x)^3}[\/latex]<\/li>\n
      4. [latex]\\dfrac{1}{\\sqrt[3]{(6b)^4}}[\/latex]<\/li>\n
      5. [latex]\\dfrac{1}{\\sqrt{(2x+3)^3}}[\/latex]<\/li>\n
      6. [latex]\\sqrt[4]{(x-3y)^3}[\/latex]<\/li>\n
      7. [latex]5^{\\frac{1}{3}}[\/latex]<\/li>\n
      8. [latex]2^{\\frac{3}{5}}[\/latex]<\/li>\n
      9. [latex](ab^5)^{\\frac{1}{3}}[\/latex] or [latex]a^{\\frac{1}{3}}b^{\\frac{5}{3}}[\/latex]<\/li>\n
      10. [latex]x^{\\frac{3}{5}}[\/latex]<\/li>\n
      11. [latex](a+5)^{\\frac{2}{3}}[\/latex]<\/li>\n
      12. [latex](a-2)^{\\frac{3}{5}}[\/latex]<\/li>\n
      13. [latex]8^{\\frac{2}{3}}\\Rightarrow (2^3)^{\\frac{2}{3}}\\Rightarrow 2^2\\text{ or }4[\/latex]<\/li>\n
      14. [latex]16^{\\frac{1}{4}}\\Rightarrow (2^4)^{\\frac{1}{4}}\\Rightarrow 2[\/latex]<\/li>\n
      15. [latex]\\sqrt[3]{4^6}\\Rightarrow (2^2)^{\\frac{6}{3}}\\Rightarrow 2^4\\text{ or }16[\/latex]<\/li>\n
      16. [latex]\\sqrt[5]{32^2}\\Rightarrow (2^5)^{\\frac{2}{5}}\\Rightarrow 2^2\\text{ or }4[\/latex]<\/li>\n
      17. [latex]x^2y^{\\frac{1}{3}+\\frac{2}{3}}\\Rightarrow x^2y[\/latex]<\/li>\n
      18. [latex]4v^{\\frac{2}{3}-1}\\Rightarrow 4v^{-\\frac{1}{3}}\\text{ or }\\dfrac{4}{v^{\\frac{1}{3}}}[\/latex]<\/li>\n
      19. [latex]{a}^{-\\frac{1}{2}}{b}^{-\\frac{1}{2}}\\Rightarrow \\dfrac{1}{{a}^{\\frac{1}{2}}{b}^{\\frac{1}{2}}}[\/latex]<\/li>\n
      20. 1<\/li>\n<\/ol>\n
          \n
        1. [latex]\\dfrac{\\cancel{a^2}\\cancel{b^0}1}{3\\cancel{a^4}a^2}\\Rightarrow \\dfrac{1}{3a^2}[\/latex]<\/li>\n
        2. [latex]\\dfrac{\\cancel{2}x^{\\frac{1}{2}}y^{\\frac{1}{3}}}{\\cancel{2}x^{\\frac{4}{3}}y^{\\frac{7}{4}}} \\Rightarrow x^{\\frac{1}{2}-\\frac{4}{3}}y^{\\frac{1}{3}-\\frac{7}{4}}\\Rightarrow x^{-\\frac{5}{6}}y^{-\\frac{17}{12}}\\Rightarrow \\dfrac{1}{x^{\\frac{5}{6}}y^{\\frac{17}{12}}}[\/latex]<\/li>\n
        3. [latex]\\dfrac{a^{\\frac{3}{4}}\\cancel{b^{-1}}b^{\\frac{7}{4}}}{3\\cancel{b^{-1}}}\\Rightarrow \\dfrac{a^{\\frac{3}{4}}b^{\\frac{7}{4}}}{3}[\/latex]<\/li>\n
        4. [latex]2x^{-2+\\frac{5}{4}-1}y^{\\frac{5}{3}+\\frac{5}{3}-\\frac{1}{2}} \\Rightarrow 2x^{-\\frac{7}{4}}y^{\\frac{17}{6}}\\Rightarrow \\dfrac{2y^{\\frac{17}{6}}}{x^{\\frac{7}{4}}}[\/latex]<\/li>\n
        5. [latex]\\dfrac{3}{2}y^{-\\frac{5}{4}- -1 - -\\frac{1}{3}} \\Rightarrow \\dfrac{3}{2}y^{\\frac{1}{12}}[\/latex]<\/li>\n
        6. [latex]\\dfrac{ab^{\\frac{1}{3}}\\cancel{2}b^{-\\frac{5}{4}}}{\\cancel{4}2a^{-\\frac{1}{2}}b^{-\\frac{2}{3}}} \\Rightarrow \\dfrac{1}{2}a^{1- -\\frac{1}{2}}b^{\\frac{1}{3}-\\frac{5}{4}- -\\frac{2}{3}} \\Rightarrow \\dfrac{1}{2}a^{\\frac{3}{2}}b^{-\\frac{1}{4}}\\Rightarrow \\dfrac{a^{\\frac{3}{2}}}{2b^{\\frac{1}{4}}}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":87,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1964","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1964","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":3,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1964\/revisions"}],"predecessor-version":[{"id":2234,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1964\/revisions\/2234"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1964\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1964"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1964"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1964"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}