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Math Help - Simplifying Question -- Please Help?

  1. #1
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    Question Simplifying Question -- Please Help?

    I have this problem to simplify with positive exponents:

    So, working with the interior brackets, I applied -3 to the equation, which resulted in:


    **because "-4" was not in brackets, the exponent was applied to the 4 only, independent of the negative sign, which resulted in -(-64), so:


    which resulted in this insane answer:


    However, when I checked it, an online calculator said the answer was:


    which means that when applying exponents to the number I did something wrong, as it should have ended up negative, which would have resulted in it becoming a positive denominator.

    What did I do wrong to end up with the wrong sign on that number?
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  2. #2
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    Re: Simplifying Question -- Please Help?

    Notice that \displaystyle \begin{align*} (-4)^{-3} = \left[ (-4)^3 \right]^{-1} = -64^{-1} = -\frac{1}{64} \end{align*}.
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    Re: Simplifying Question -- Please Help?

    Awesome, thanks, I understand now!
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