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Math Help - exponent and bases

  1. #1
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    another one...help!

    Rewrite (1/27)^x as a base of three.....

    HELP!
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  2. #2
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    Quote Originally Posted by Luckyjoshua
    Rewrite (1/27)^x as a base of three.....

    HELP!
    27 = 3^3 so...

    \left ( \frac{1}{27} \right ) ^x = \left ( \frac{1}{3^3} \right ) ^x

     = \left ( \left [ \frac{1}{3} \right ]  ^3 \right )^x

     = \left ( \frac{1}{3} \right ) ^{3 \cdot x} = \left ( \frac{1}{3} \right ) ^{3x}

    Again, \frac{1}{3} = 3^{-1} which results (via the same kind of method) to

    \left ( \frac{1}{27} \right ) ^x = 3^{-3x}

    -Dan
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