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Math Help - Trouble with exponential equations

  1. #1
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    Trouble with exponential equations

    The problem in particular I'm having trouble with is x^(-2/3) = (1/4).

    I think I did everything correctly when I got stuck at x^1 = (1/4)^(-3/2)

    Since I'm new to the MATH tags, that's supposed to be:

    x^(-2/3) = (1/4)
    and
    x^1 = (1/4)^(-3/2), respectively.

    Would I continue on to x = 4^(2/3) (x = 4^(2/3))which would be simple from there, or another method?
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  2. #2
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    Quote Originally Posted by fkhnksaha View Post
    The problem in particular I'm having trouble with is x^(-2/3) = (1/4).

    I think I did everything correctly when I got stuck at x^1 = (1/4)^(-3/2)

    Since I'm new to the MATH tags, that's supposed to be:

    x^(-2/3) = (1/4)
    and
    x^1 = (1/4)^(-3/2), respectively.

    Would I continue on to x = 4^(2/3) (x = 4^(2/3))which would be simple from there, or another method?
    \left(\frac{1}{4}\right)^{-3/2} = \left(4^{-1}\right)^{-3/2} = 4^{3/2} = \left(4^{1/2}\right)^3 = 2^3 = 8.
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  3. #3
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    Thanks a million for the quick reply! This definitely helped my understanding of reciprocals and negative exponents!
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