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Math Help - exponents help #2

  1. #1
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    exponents help #2

    -81^{-3/4}

    My steps:

    = 1 / (-81^3) ^ {1/4}

    = 1 / (-531441) ^ {1/4}

    = 1 / (something impossible)

    My book's answer:

    - 1/27

    Should my first step really be:

    - 1 / (81^3) ^ {1/4}?
    Last edited by mr fantastic; July 6th 2010 at 12:35 AM. Reason: Edited title.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    -81^{-3/4}=(-3^4)^{-3/4}=-3^{4\cdot {-3/4}}=-3^{-3}=(-\frac{1}{3})^3=-\frac{1}{27}
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  3. #3
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    so is - x^y = -(x^y)?, not (-x)^y
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    The first one, yes.
    In second one, you can't "work" with y-ies that are not integers...
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