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Math Help - Exponents

  1. #1
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    Exponents

    The value of (32/243)^-3/5 is
    (a)27/8
    (b)8/27
    (c)16/27
    Pls explain.
    Last edited by devi; August 18th 2008 at 09:37 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by devi View Post
    The value of (32/243)^-3/5 is
    (a)27/8
    (b)8/27
    (c)16/27
    Pls explain.
    32=2^5 and 243=3^5, so:

    (32/243)^(-3/5)=(2/3)^(-3)=(3/2)^3=27/8

    RonL
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  3. #3
    o_O
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    Remember that: \displaystyle a^{\frac{s}{t}} = \displaystyle \sqrt[t]{a^{s}} = \displaystyle\left(\sqrt[t]{a}\right)^{s}

    Here,
    \left(\frac{32}{243}\right)^{-\frac{3}{5}} = \underbrace{\left(\frac{243}{32}\right)^{\frac{3}{  5}}}_{\displaystyle a^{-m} = \displaystyle \frac{1}{a^{ m}}} = \left(\frac{243^{3/5}}{32^{3/5}}\right) = ...

    Can you finish?
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