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Math Help - exponentiation

  1. #1
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    exponentiation

    We have to compute this .. on a computer
    exponentiation-aaamath.png
    seems very easy, but me and my partner cant agree on something
    -------------------

    I say that this is to be see as

    X = bm/n

    b being negative and n being even, the answer is the complex number 5i
    --------------------
    my partner says:

    this should be see as

    X = (bm)1/n

    giving the answer 5 and -5
    ---------------------

    I say that he is wrong because:
    if I reverse the function,

    ((-5)4)1/2 = 25, not -25
    ((-5)1/2)4 = 25, not -25

    -----------------------
    and

    ((5i)1/2)4 = -25
    ----------------------

    but he wont see this as a proof since the programs "Maple" and also "Microsoft Math" does return 5 and -5
    ----------------------

    Please, tell me who is right ??
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  2. #2
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    Re: exponentiation

    Quote Originally Posted by LChenier View Post
    We have to compute this .. on a computer
    Click image for larger version. 

Name:	AAAMath.png 
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    Oh come on! Anyone with very very basic algebra skills knows that:

    \sqrt[4]{{{x^2}}} = \sqrt {\left| x \right|} .

    If that leaves you (or anyone) clueless, please consult any middle-school mathematics teacher.
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  3. #3
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    Re: exponentiation

    I know that, but:

    sqtr(|-25|) = 5

    then why

    5^2 <> -25
    (5^(1/2))^4 <> -25

    why

    the 4th root of -5 is sqrt(5i) and sqrt(5i)^2 = 5i

    where now,

    (5i^(1/2))^4 = -25
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