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Math Help - negative fractions to negative exponents

  1. #1
    Member
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    negative fractions to negative exponents

    What is the proper method to solve this:

    (-)^-3

    Method A:

    (-)^-3

    = (-1^-3)/(2^-3)

    = (2^3)/(-1^3)

    = 8/-1

    = -8

    Method B:

    (-)^-3

    = (1^-3)/(-2^-3)

    = (-2^3)/(1^3)

    = -8/1

    = -8

    Should the negative be placed in the "1" as in method A or in the "2" as in method B? This gets confusing as the question is not written in the form of (-1/2) or (1/-2) but as (-) where the negative appeared to be shared by both 1 and 2. Or it doesn't matter?

    Please help with this basic question. I never had high school math. Thanks.
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  2. #2
    MHF Contributor Quick's Avatar
    Joined
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    New England
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    Both ways work.

    Just to clarify: (-1)/(2)=(1)/(-2)

    The proof: you know that: (1/2)x(2/3)=(1x2)/(2x3)=2/6=1/3

    and you know that: -1x-1=1

    and you know that: -1/-1=1

    then: (-1)/(2)=(-1)/(2)

    multiply both sides by 1: (-1)/(2)x1=(-1)/(2)x(-1)/(-1)

    thus: (-1)/(2)=(-1x-1)/(2x-1)

    therefore: (-1)/(2)=(1)/(-2)
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  3. #3
    Member
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    Quote Originally Posted by Quick View Post
    Both ways work.
    Thanks again for confirming. And that was quick too!

    Cheers.
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