Answer Key 6.1

  1. 4^{1+4+4}=4^9\text{ or }262,144
  2. 4^{1+4+2}=4^7\text{ or }16,384
  3. 2\cdot 4\cdot m^{4+2}n^{2+1}=8m^6n^3
  4. x^{2+1}y^{4+2}=x^3y^6
  5. 3^{3\cdot 4}=3^{12}\text{ or }531,441
  6. 4^{3\cdot 4}=4^{12}\text{ or }16,772,216
  7. 2^2u^{3\cdot 2}v^{2\cdot 2}=4u^6v^4
  8. x^3y^3
  9. 4^{5-3}=4^2\text{ or }16
  10. 3^{7-3}=3^4\text{ or }81
  11. 3^{1-1}n^{1-1}m^2=\cancel{3^0} \cancel{n^0} m^2
  12. 4^{-1}x^{2-1}y^{4-1}=4^{-1}xy^3
  13. (2x^{2+3}y^{4+3})^2
    (2x^5y^7)^2
    2^2x^{5\cdot 2}y^{7\cdot 2}
    4x^{10}y^{14}
  14. [2u^{2+4}v^2]^3
    [2u^6v^2]^3
    2^3u^{6\cdot 3}v^{2\cdot 3} \Rightarrow 8u^{18}v^6
  15. [2^3x^3\div x^3]^2
    [2^3x^{3-3}]^2
    2^{3\cdot 2}\cancel{x^0}
    2^6 \text{ or }64
  16. 2a^{2+7}b^2\div b^2a^{4\cdot 2}
    2a^9b^2\div b^2a^8
    2a^{9-8}\cancel{b^{2-2}}
    2a
  17. [2y^{17}\div 2^4x^{2\cdot 4}y^{4\cdot 4}]^3
    [2y^{17}\div 2^4x^8y^{16}]^3
    [2^{1-4}y^{17-16}x^{-8}]^3
    [2^{-3}yx^{-8}]^3
    2^{-9}y^3x^{-24}
  18. [xy^2\cdot y^8]\div 2y^4
    xy^{10}\div 2y^4
    2^{-1}xy^{10-4}
    2^{-1}xy^6
  19. 4x^3y^8\div 2xy^7
    2x^2y
  20. 2y^3x^2\div x^4y^4
    2x^{-2}y^{-1}
  21. [q^3r^2\cdot 4p^4q^4r^6]\div 2p^3
    4p^4q^7r^8\div 2p^3
    2pq^7r^8
  22. 4x^6y^{12}z^{10}\div x^4y^8z^8
    4x^2y^4z^2

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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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