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Thread: [SOLVED] Problem with Exponential Equations

  1. #1
    Junior Member
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    [SOLVED] Problem with Exponential Equations

    Hi, I'm having trouble with how to do this question. It's quite simple but for some reason I'm not doing it right... Here it is: The exact edge length of a cube is (\frac{5}{2})^{-2/3} units. Determine the volume of the cube.

    I know that the volume is equal to (side length x side length x side length) or in other words (side length) cubed. However, i can't get the same answer as the book states which is:
    \frac{4}{25} cubed. I started out by cubing (^3) the whole side length but somehow ended up with the wrong answer.

    If someone could show me the steps in doing this so i can find out where i went wrong, that would be great! THANKS!
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  2. #2
    MHF Contributor
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    Hi

    \left(\left(\frac{5}{2}\right)^{-\frac{2}{3}}\right)^3 = \left(\frac{5}{2}\right)^{-\frac{2}{3}\cdot 3} = \left(\frac{5}{2}\right)^{-2} = \left(\frac{2}{5}\right)^{2} = \frac{4}{25}

    Remember

    \left(a^n\right)^p = a^{np}

    a^{-n} = \frac{1}{a^n} = \left(\frac{1}{a}\right)^n
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  3. #3
    Junior Member
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    Oh i see. What I did wrong was distributing the ^3 into the 5/2 AND -3/2, thanks so much.
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