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Math Help - Negative and rational powers

  1. #1
    Member Mr Rayon's Avatar
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    Negative and rational powers

    Simplify the following, expressing your answer with positive index numbers

     <br />
\frac{(-2)^{-3}\times2^{-4}}{2^{-3}}<br /> <br />

    Please show complete working out. Any help will be appreciated!
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  2. #2
    Super Member
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    For even exponents n, (-a)^n = a^n.
    For odd exponents n, (-a)^n = -a^n.

    You should also know the properties of exponents, like
    a^m \times a^n = a^{m + n}
    and
    \frac{a^m}{a^n} = a^{m - n}.

    Apply the above to the problem. (I get -\frac{1}{2^4} or -\frac{1}{16} as my answer.)


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  3. #3
    MHF Contributor

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    Quote Originally Posted by Mr Rayon View Post
    Simplify the following, expressing your answer with positive index numbers

     <br />
\frac{(-2)^{-3}\times2^{-4}}{2^{-3}}<br /> <br />

    Please show complete working out. Any help will be appreciated!
    First, (-2)^{-3}= (-1(2))^{-3}= (-1)^{-3}2^{-3} and (-1)^3= -1
    a^{-3}= 1/a^3 so this is the same as -(2^{-3})(2^{-4})(2^3). Now use the fact that a^na^m= a^{n+m}.
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