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Math Help - [SOLVED] Fractional Exponents

  1. #1
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    Question [SOLVED] Fractional Exponents

    Can someone please help me solve

    81^3/4
    __

    16

    Hopefully this displays correctly. In case it doesn't here it is again:
    (81 / 16)^(3 / 4)

    I can solve it with the calculator obviously (3 3/8), but I need to demonstrate it and I can't figure out how.

    Thank you so much for your help!

    Neenoon
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  2. #2
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    If x is positive, p and q are integers where q is positive then,
    x^(p/q)= q root of (x^p).

    So (81/16)^(3/4) = 4 root of [ (81/16)^(3) ] = 27/8 or 3 3/8.
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  3. #3
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    Hello, Neenoon!

    Simplify: .(81/16)^{}
    We have: .(81)^{} / (16)^{}

    Since .81 = 3^4 .and .16 = 2^4,

    . . we have: .(3^4)^{} / (2^4)^{} .= .(3^3) / (2^3) .= .27/8

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  4. #4
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    I understand the demonstration. Thank you both so much, this prooves very useful.
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