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Math Help - How to work a fractional exponent? Need non decimal answer!

  1. #1
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    How to work a fractional exponent? Need non decimal answer!

    So on a recent test I ran into this, I wasnt sure how to work the first part because I couldnt figure out the fraction for it.

    The question said to
    PI((4/5(4)^5/4)-(16/3))

    My first instinct is to solve the first, then subtract the second from it then multiply it by PI, however I couldnt figure out how to turn the first into a fractional answer.

    Any help is appreciated.

    Thanks
    Rich
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  2. #2
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    Hint:

    \displaystyle a^{\frac{5}{4}} = \sqrt[4]{a^5} = \sqrt[4]{a^4\cdot a} = \sqrt[4]{a^4}\cdot \sqrt[4]{a} = a\sqrt[4]{a}.
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  3. #3
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    Quote Originally Posted by Spoolx View Post
    So on a recent test I ran into this, I wasnt sure how to work the first part because I couldnt figure out the fraction for it.

    The question said to
    PI((4/5(4)^5/4)-(16/3))

    My first instinct is to solve the first, then subtract the second from it then multiply it by PI, however I couldnt figure out how to turn the first into a fractional answer.

    Any help is appreciated.

    Thanks
    Rich
    4^{5/4}=(4^{1/4})^5=(\sqrt{2})^5=4\sqrt{2}

    If we are interested in the positive and negative values there would be a \pm in front

    CB
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