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Math Help - Negative fraction powers

  1. #1
    Member GAdams's Avatar
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    Negative fraction powers

    Evaluate 1000^ -2/3
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by GAdams View Post
    Evaluate 1000^ -2/3
     1000^{\frac{-2}{3}}

     = \sqrt[3]{1000^{-2}}

     = 10^{-2}

     = \frac{1}{100}
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  3. #3
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    Hello, GAdams!

    I must assume you know the necessary basics . . .


    Evaluate: . 1000^{-\frac{2}{3}}

    We have: . 1000^{-\frac{2}{3}} \;=\;\frac{1}{1000^{\frac{2}{3}}}

    Since 1000 \,=\,10^3, the denominator is: . \left(10^3\right)^{\frac{2}{3}} \:=\:10^{(3\cdot\frac{2}{3})}\:=\:10^2\:=\:100

    Answer: . \frac{1}{100}

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