Honors Algebra 2: Extra Practice on Positive and Negative Exponents

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Simplify the following. Express your answer using only positive exponents.

  1. \( \displaystyle \left( -7u^{2}\right) \left( 5u^{8}\right) \)
    2. Solution

    \( -35u^{10}\)

  2. \( \displaystyle \left( -8v^{3}\right) \left( -6v^{-9}\right) \)
    3. Solution

    \( \displaystyle \frac{ 48}{v^{6}}\)

  3. \( \displaystyle \left( 2x^{4}y^{-7}\right) \left( 3x^{-1}y^{5}\right) \)
    4. Solution

    \( \displaystyle \frac{6x^{3}}{y^{2}}\)

  4. \( \displaystyle \left( 9z^{6}w^{8}\right) \left( -5z^{-6}w^{-11}\right) \)
    5. Solution

    \( \displaystyle -\frac{45}{w^{3}}\)

  5. \( \displaystyle \left( 5a^{-3}a^{-2}b^{-1}\right) \left( -25a^{6}b^{-4}\right) \)
    6. Solution

    \( \displaystyle -\frac{125a}{b^{5}}\)

  6. \( \displaystyle \left( -3p^{4}q^{-3}\right) ^{2} \left( 4p^{-5}q^{7}\right) \)
    7. Solution

    \( 36p^{3}q\)

  7. \( \displaystyle \left( \frac{3}{4} d^{3}e^{-5}\right) ^{-2}\)
    8. Solution

    \( \displaystyle \frac{16e^{10}}{9d^{6}}\)

  8. \( \displaystyle \left( \frac{1}{2} a^{2}b^{3}\right) ^{4} \left( a^{-5}b^{-10}\right) \)
    9. Solution

    \( \displaystyle \frac{a^{3}b^{2}}{16}\)

  9. \( \displaystyle \left( 6x^{8}y^{-9}\right) \left( x^{-2}y^{-3}\right) ^{3}\)
    10. Solution

    \( \displaystyle \frac{6x^{2}}{y^{18}}\)

  10. \( \displaystyle \left( -v^{7}w^{-8}\right) ^{3} \left( -v^{-9}w^{6}\right) ^{4}\)
    11. Solution

    \( \displaystyle -\frac{1}{v^{15}}\)

  11. \( \displaystyle \left( u^{6}\right) ^{-4} \left( u^{3}\right) ^{8}\)
    12. Solution

    \( 1\)

  12. \( \displaystyle \left( ab\right) ^{-7} \left( a^{3}b^{-2}\right) ^{4}\)
    13. Solution

    \( \displaystyle \frac{a^{5}}{b^{15}}\)

  13. \( \displaystyle \frac{c^{4}d^{-3}}{c^{3}d} \)
    14. Solution

    \( \displaystyle \frac{c}{d^{4}}\)

  14. \( \displaystyle \left( \frac{f^{5}g^{-3}}{g^{-5}}\right) ^{2}\)
    15. Solution

    \( f^{10}g^{4}\)

  15. \( \displaystyle \frac{\left( 2r^{3}s^{-3} \right) ^{5}}{ \left( 4r^{7}s^{-10}\right)} \)
    16. Solution

    \( \displaystyle \frac{8r^{8}}{s^{5}}\)

  16. \( \displaystyle \frac{25x^{-5}y^{3}}{ \left( 5x^{2}y\right) ^{-3}}\)
    17. Solution

    \( 3125xy^{6}\)

  17. \( \displaystyle \left( \frac{3u^{-4}v^{3}}{ 2u^{-5}v} \right) ^{-2}\)
    18. Solution

    \( \displaystyle \frac{4}{9u^{2}v^{4}}\)

  18. \( \displaystyle \left( - \frac{a^{-2}b^{-1}}{3a^{-3}b^{3}} \right) ^{-4}\)
    19. Solution

    \( \displaystyle \frac{81b^{16}}{a^{4}}\)

  19. \( \displaystyle \frac{a^{m + 1}}{a^{m - 1}}\)
    20. Solution

    \( a^{2}\)

  20. \( \displaystyle \left( b^{2 - p}b^{2+p}\right) ^{2}\)
    21. Solution

    \( b^{8}\)

  21. \( \displaystyle 5 \left( 5^{e+1}\right) ^{e-1}\)
    22. Solution

    \( 5^{e^2}\)