{"id":1865,"date":"2021-12-02T19:39:47","date_gmt":"2021-12-03T00:39:47","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-6-2\/"},"modified":"2023-09-01T12:57:02","modified_gmt":"2023-09-01T16:57:02","slug":"answer-key-6-2","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-6-2\/","title":{"raw":"Answer Key 6.2","rendered":"Answer Key 6.2"},"content":{"raw":"
    \r\n \t
  1. [latex]2x^4y^{-2}\\cdot 2^4x^4y^{12}[\/latex]\r\n[latex]2^5x^8y^{10}\\Rightarrow 32x^8y^{10}[\/latex]<\/li>\r\n \t
  2. [latex]2a^{-2}b^{-3}\\cdot 2^4b^{16}[\/latex]\r\n[latex]32a^{-2}b^{13}\\Rightarrow \\dfrac{32b^{13}}{a^2}[\/latex]<\/li>\r\n \t
  3. [latex]2^4x^8y^8\\cdot x^{-4}[\/latex]\r\n[latex]2^4x^4y^8\\Rightarrow 16x^4y^8[\/latex]<\/li>\r\n \t
  4. 1<\/li>\r\n \t
  5. [latex]2x^{-3--3}y^{2-3}3^{-2}[\/latex]\r\n[latex]2\\cancel{x^0}y^{-1}3^{-2}\\Rightarrow \\dfrac{2}{9y}[\/latex]<\/li>\r\n \t
  6. [latex]3y^3\\div [6x^7y^{-2}][\/latex]\r\n[latex]3x^{-7}y^{3--2}\\div 6[\/latex]\r\n[latex]3x^{-7}y^5\\div 6 \\Rightarrow \\dfrac{y^5}{2x^7}[\/latex]<\/li>\r\n \t
  7. [latex]2y\\div y^8[\/latex]\r\n[latex]2y^{1-8}[\/latex]\r\n[latex]2y^{-7}\\Rightarrow \\dfrac{2}{y^7}[\/latex]<\/li>\r\n \t
  8. [latex]a^{16}\\div 2b\\Rightarrow \\dfrac{a^{16}}{2b}[\/latex]<\/li>\r\n \t
  9. [latex]2^4a^8b^{12}\\div a^{-1}[\/latex]\r\n[latex]16a^{8+1}b^{12}[\/latex]\r\n[latex]16a^9b^{12}[\/latex]<\/li>\r\n \t
  10. [latex]{2}^{-2}{y}^{8}\\div {x}^{2}\\Rightarrow \\dfrac{{y}^{8}}{{2}^{2}{x}^{2}}\\Rightarrow \\dfrac{{y}^{8}}{{4x}^{2}}[\/latex]<\/li>\r\n \t
  11. [latex]2^4m^4n^{4--2}[\/latex]\r\n[latex]16m^4n^6[\/latex]<\/li>\r\n \t
  12. [latex]2x^{-3}\\div x^{-4}y^3[\/latex]\r\n[latex]2x^{-3--4}y^{-3}\\Rightarrow 2xy^{-3} \\Rightarrow \\dfrac{2x}{y^3}[\/latex]<\/li>\r\n \t
  13. [latex][2u^{-2}v^3\\cdot 2^{-1}u^{-1}v^{-4}]\\div 2u^{-4}[\/latex]\r\n[latex][u^{-3}v^{-1}]\\div 2u^{-4}[\/latex]\r\n[latex]2^{-1}u^{-3--4}v^{-1}[\/latex]\r\n[latex]2^{-1}uv^{-1}\\Rightarrow \\dfrac{u}{2v}[\/latex]<\/li>\r\n \t
  14. [latex]2y \\div 2^{-1}y^{-4}[\/latex]\r\n[latex]2y\\cdot 2y^4 \\Rightarrow 4y^5[\/latex]<\/li>\r\n \t
  15. [latex]b^{-1}\\div 2a^{-3}b^2[\/latex]\r\n[latex]b^{-1}\\cdot 2^{-1}a^3b^{-2}\\Rightarrow \\dfrac{a^3}{2b^3}[\/latex]<\/li>\r\n \t
  16. [latex]2x^2yz \\div [2x^4y^4z^{-2}z^4y^8][\/latex]\r\n[latex]2x^2yz \\div [2x^4y^{12}z^2][\/latex]\r\n[latex]2x^2yz \\cdot z^{-1}x^{-4}y^{-12}z^{-2}[\/latex]\r\n[latex]x^{-2}y^{-11}z^{-1}\\Rightarrow \\dfrac{1}{x^2y^{11}z}[\/latex]<\/li>\r\n \t
  17. [latex]2a^{-3}b^2c^2b^6\\div a^9b^{-6}c^9[\/latex]\r\n[latex]2a^{-3}b^8c^2\\cdot a^{-9}b^6c^{-9}[\/latex]\r\n[latex]2a^{-12}b^{14}c^{-7}\\Rightarrow \\dfrac{2b^{14}}{a^{12}c^7}[\/latex]<\/li>\r\n \t
  18. [latex]2m^2p^2q^5 \\div [2^3m^3\\cdot 4^3p^6][\/latex]\r\n[latex]2m^2p^2q^5 \\div [2^3m^3\\cdot 2^6p^6][\/latex]\r\n[latex]2m^2p^2q^5 \\div 2^9m^3p^6[\/latex]\r\n[latex]2m^2p^2q^5\\cdot 2^{-9}m^{-3}p^{-6}[\/latex]\r\n[latex]2^{-8}m^{-1}p^{-4}q^5\\Rightarrow \\dfrac{q^5}{2^8mp^4}\\Rightarrow \\dfrac{q^5}{256mp^4}[\/latex]<\/li>\r\n \t
  19. [latex]y^{-1}x^4z^{-2}\\div x^2y^3z^2[\/latex]\r\n[latex]y^{-1}x^4z^{-2}\\cdot x^{-2}y^{-3}z^{-2}[\/latex]\r\n[latex]x^2y^{-4}z^{-4}\\Rightarrow \\dfrac{x^2}{y^4z^4}[\/latex]<\/li>\r\n \t
  20. [latex]2mpn^{-3}\\div 2n^2n^{-12}p^6[\/latex]\r\n[latex]2mpn^{-3}\\div 2n^{-10}p^6[\/latex]\r\n[latex]2mpn^{-3}\\cdot 2^{-1}n^{10}p^{-6}[\/latex]\r\n[latex]mp^{-5}n^7\\Rightarrow \\dfrac{mn^7}{p^5}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]2x^4y^{-2}\\cdot 2^4x^4y^{12}[\/latex]
      \n[latex]2^5x^8y^{10}\\Rightarrow 32x^8y^{10}[\/latex]<\/li>\n
    2. [latex]2a^{-2}b^{-3}\\cdot 2^4b^{16}[\/latex]
      \n[latex]32a^{-2}b^{13}\\Rightarrow \\dfrac{32b^{13}}{a^2}[\/latex]<\/li>\n
    3. [latex]2^4x^8y^8\\cdot x^{-4}[\/latex]
      \n[latex]2^4x^4y^8\\Rightarrow 16x^4y^8[\/latex]<\/li>\n
    4. 1<\/li>\n
    5. [latex]2x^{-3--3}y^{2-3}3^{-2}[\/latex]
      \n[latex]2\\cancel{x^0}y^{-1}3^{-2}\\Rightarrow \\dfrac{2}{9y}[\/latex]<\/li>\n
    6. [latex]3y^3\\div [6x^7y^{-2}][\/latex]
      \n[latex]3x^{-7}y^{3--2}\\div 6[\/latex]
      \n[latex]3x^{-7}y^5\\div 6 \\Rightarrow \\dfrac{y^5}{2x^7}[\/latex]<\/li>\n
    7. [latex]2y\\div y^8[\/latex]
      \n[latex]2y^{1-8}[\/latex]
      \n[latex]2y^{-7}\\Rightarrow \\dfrac{2}{y^7}[\/latex]<\/li>\n
    8. [latex]a^{16}\\div 2b\\Rightarrow \\dfrac{a^{16}}{2b}[\/latex]<\/li>\n
    9. [latex]2^4a^8b^{12}\\div a^{-1}[\/latex]
      \n[latex]16a^{8+1}b^{12}[\/latex]
      \n[latex]16a^9b^{12}[\/latex]<\/li>\n
    10. [latex]{2}^{-2}{y}^{8}\\div {x}^{2}\\Rightarrow \\dfrac{{y}^{8}}{{2}^{2}{x}^{2}}\\Rightarrow \\dfrac{{y}^{8}}{{4x}^{2}}[\/latex]<\/li>\n
    11. [latex]2^4m^4n^{4--2}[\/latex]
      \n[latex]16m^4n^6[\/latex]<\/li>\n
    12. [latex]2x^{-3}\\div x^{-4}y^3[\/latex]
      \n[latex]2x^{-3--4}y^{-3}\\Rightarrow 2xy^{-3} \\Rightarrow \\dfrac{2x}{y^3}[\/latex]<\/li>\n
    13. [latex][2u^{-2}v^3\\cdot 2^{-1}u^{-1}v^{-4}]\\div 2u^{-4}[\/latex]
      \n[latex][u^{-3}v^{-1}]\\div 2u^{-4}[\/latex]
      \n[latex]2^{-1}u^{-3--4}v^{-1}[\/latex]
      \n[latex]2^{-1}uv^{-1}\\Rightarrow \\dfrac{u}{2v}[\/latex]<\/li>\n
    14. [latex]2y \\div 2^{-1}y^{-4}[\/latex]
      \n[latex]2y\\cdot 2y^4 \\Rightarrow 4y^5[\/latex]<\/li>\n
    15. [latex]b^{-1}\\div 2a^{-3}b^2[\/latex]
      \n[latex]b^{-1}\\cdot 2^{-1}a^3b^{-2}\\Rightarrow \\dfrac{a^3}{2b^3}[\/latex]<\/li>\n
    16. [latex]2x^2yz \\div [2x^4y^4z^{-2}z^4y^8][\/latex]
      \n[latex]2x^2yz \\div [2x^4y^{12}z^2][\/latex]
      \n[latex]2x^2yz \\cdot z^{-1}x^{-4}y^{-12}z^{-2}[\/latex]
      \n[latex]x^{-2}y^{-11}z^{-1}\\Rightarrow \\dfrac{1}{x^2y^{11}z}[\/latex]<\/li>\n
    17. [latex]2a^{-3}b^2c^2b^6\\div a^9b^{-6}c^9[\/latex]
      \n[latex]2a^{-3}b^8c^2\\cdot a^{-9}b^6c^{-9}[\/latex]
      \n[latex]2a^{-12}b^{14}c^{-7}\\Rightarrow \\dfrac{2b^{14}}{a^{12}c^7}[\/latex]<\/li>\n
    18. [latex]2m^2p^2q^5 \\div [2^3m^3\\cdot 4^3p^6][\/latex]
      \n[latex]2m^2p^2q^5 \\div [2^3m^3\\cdot 2^6p^6][\/latex]
      \n[latex]2m^2p^2q^5 \\div 2^9m^3p^6[\/latex]
      \n[latex]2m^2p^2q^5\\cdot 2^{-9}m^{-3}p^{-6}[\/latex]
      \n[latex]2^{-8}m^{-1}p^{-4}q^5\\Rightarrow \\dfrac{q^5}{2^8mp^4}\\Rightarrow \\dfrac{q^5}{256mp^4}[\/latex]<\/li>\n
    19. [latex]y^{-1}x^4z^{-2}\\div x^2y^3z^2[\/latex]
      \n[latex]y^{-1}x^4z^{-2}\\cdot x^{-2}y^{-3}z^{-2}[\/latex]
      \n[latex]x^2y^{-4}z^{-4}\\Rightarrow \\dfrac{x^2}{y^4z^4}[\/latex]<\/li>\n
    20. [latex]2mpn^{-3}\\div 2n^2n^{-12}p^6[\/latex]
      \n[latex]2mpn^{-3}\\div 2n^{-10}p^6[\/latex]
      \n[latex]2mpn^{-3}\\cdot 2^{-1}n^{10}p^{-6}[\/latex]
      \n[latex]mp^{-5}n^7\\Rightarrow \\dfrac{mn^7}{p^5}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":50,"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-1865","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\/1865","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\/1865\/revisions"}],"predecessor-version":[{"id":2207,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1865\/revisions\/2207"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1865\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1865"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1865"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1865"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}