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Math Help - negative exponents

  1. #1
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    negative exponents

    I am lost on this problem.
    -2^-3
    The answer goes like this:
    -1/2^3
    I think I understand up to here. But where does the double negative come in on this next step?
    --1/2*2*2
    --1/4*2
    --1/8
    -*8/8-1/8
    -8/8-1/8
    -8-1/8
    -9/8
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  2. #2
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    Quote Originally Posted by Jerry Cunningham View Post
    I am lost on this problem.
    -2^-3
    The answer goes like this:
    -1/2^3
    I think I understand up to here. But where does the double negative come in on this next step?
    --1/2*2*2
    --1/4*2
    --1/8
    -*8/8-1/8
    -8/8-1/8
    -8-1/8
    -9/8
    -2^{-3}

    The exponent only applies to the base in this case the 2 NOT the negative sign.

    If you like you can think of it this way.

    (-1)2^{-3}=\underbrace{\frac{-1}{2^3}}_{\mbox{Law of neg exp.}}=\frac{-1}{8}
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  3. #3
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    Quote Originally Posted by Jerry Cunningham View Post
    ...But where does the double negative come in on this next step?
    -1-1/2*2*2
    -1-1/4*2
    -1-1/8
    -*8/8-1/8
    -8/8-1/8
    -8-1/8
    -9/8
    I assume that there is a typo.
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  4. #4
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    Quote Originally Posted by Jerry Cunningham View Post
    I am lost on this problem.
    -2^-3
    The answer goes like this:
    -1/2^3
    I think I understand up to here. But where does the double negative come in on this next step?
    --1/2*2*2
    --1/4*2
    --1/8
    -*8/8-1/8
    -8/8-1/8
    -8-1/8
    -9/8
    That's very wrong

    according to the question we need to find what -2^-3 is,

    now get rid of the negative integer by converting the base(-2) to a fraction

    so this implies (1/-2)^3

    now it's easy, the answer is 1/-8

    but we need to convert this to standard from, so we multiply both sides of the fraction by -1

    so the final answer is -1/8

    next time, try separating the exponents from the base with a parenthesis

    Last edited by ice_syncer; April 2nd 2008 at 04:54 AM. Reason: forgot the minus sign
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