Answer Key 6.2

  1. 2x^4y^{-2}\cdot 2^4x^4y^{12}
    2^5x^8y^{10}\Rightarrow 32x^8y^{10}
  2. 2a^{-2}b^{-3}\cdot 2^4b^{16}
    32a^{-2}b^{13}\Rightarrow \dfrac{32b^{13}}{a^2}
  3. 2^4x^8y^8\cdot x^{-4}
    2^4x^4y^8\Rightarrow 16x^4y^8
  4. 1
  5. 2x^{-3--3}y^{2-3}3^{-2}
    2\cancel{x^0}y^{-1}3^{-2}\Rightarrow \dfrac{2}{9y}
  6. 3y^3\div [6x^7y^{-2}]
    3x^{-7}y^{3--2}\div 6
    3x^{-7}y^5\div 6 \Rightarrow \dfrac{y^5}{2x^7}
  7. 2y\div y^8
    2y^{1-8}
    2y^{-7}\Rightarrow \dfrac{2}{y^7}
  8. a^{16}\div 2b\Rightarrow \dfrac{a^{16}}{2b}
  9. 2^4a^8b^{12}\div a^{-1}
    16a^{8+1}b^{12}
    16a^9b^{12}
  10. 2^{-2}y^{8}\div x^2\Rightarrow \dfrac{y&8}{2^2x^2}\Rightarrow \dfrac{y^8}{4x^2}
  11. 2^4m^4n^{4--2}
    16m^4n^6
  12. 2x^{-3}\div x^{-4}y^3
    2x^{-3--4}y^{-3}\Rightarrow 2xy^{-3} \Rightarrow \dfrac{2x}{y^3}
  13. [2u^{-2}v^3\cdot 2^{-1}u^{-1}v^{-4}]\div 2u^{-4}
    [u^{-3}v^{-1}]\div 2u^{-4}
    2^{-1}u^{-3--4}v^{-1}
    2^{-1}uv^{-1}\Rightarrow \dfrac{u}{2v}
  14. 2y \div 2^{-1}y^{-4}
    2y\cdot 2y^4 \Rightarrow 4y^5
  15. b^{-1}\div 2a^{-3}b^2
    b^{-1}\cdot 2^{-1}a^3b^{-2}\Rightarrow \dfrac{a^3}{2b^3}
  16. 2x^2yz \div [2x^4y^4z^{-2}z^4y^8]
    2x^2yz \div [2x^4y^{12}z^2]
    2x^2yz \cdot z^{-1}x^{-4}y^{-12}z^{-2}
    x^{-2}y^{-11}z^{-1}\Rightarrow \dfrac{1}{x^2y^{11}z}
  17. 2a^{-3}b^2c^2b^6\div a^9b^{-6}c^9
    2a^{-3}b^8c^2\cdot a^{-9}b^6c^{-9}
    2a^{-12}b^{14}c^{-7}\Rightarrow \dfrac{2b^{14}}{a^{12}c^7}
  18. 2m^2p^2q^5 \div [2^3m^3\cdot 4^3p^6]
    2m^2p^2q^5 \div [2^3m^3\cdot 2^6p^6]
    2m^2p^2q^5 \div 2^9m^3p^6
    2m^2p^2q^5\cdot 2^{-9}m^{-3}p^{-6}
    2^{-8}m^{-1}p^{-4}q^5\Rightarrow \dfrac{q^5}{2^8mp^4}\Rightarrow \dfrac{q^5}{256mp^4}
  19. y^{-1}x^4z^{-2}\div x^2y^3z^2
    y^{-1}x^4z^{-2}\cdot x^{-2}y^{-3}z^{-2}
    x^2y^{-4}z^{-4}\Rightarrow \dfrac{x^2}{y^4z^4}
  20. 2mpn^{-3}\div 2n^2n^{-12}p^6
    2mpn^{-3}\div 2n^{-10}p^6
    2mpn^{-3}\cdot 2^{-1}n^{10}p^{-6}
    mp^{-5}n^7\Rightarrow \dfrac{mn^7}{p^5}

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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