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Math Help - Exponents for exponents

  1. #1
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    Exponents for exponents

    Hi,

    I just stumbled on a problem in my math work.

    My job is to simplify/reduce the following exponentiation:
    4^(x+1)x-1

    My solution for it is following:

    4^(x+1)x-1​ = 4^(x+1)(x-1) = 4^x2-1

    But I got a feeling, that it's wrong. So I want to know, what I'm doing wrong.

    Thanks.
    Last edited by JrAl; September 24th 2012 at 10:35 AM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Exponents for exponents

    If you are given:

    \left(4^{x+1} \right)^{x-1}

    then what you've done is correctly apply the property of exponents (a^b)^c=a^{bc}.

    However, if you are given:

    4^{(x+1)^{x-1}}

    then there isn't much you can do to simplify that I know of.
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  3. #3
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    Re: Exponents for exponents

    The one I was given is the second one.

    I'm thinking of basing it on am*an=am+n and a-n=1/an but can't seem to figure it out.
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Exponents for exponents

    Quote Originally Posted by JrAl View Post
    Hi,

    I just stumbled on a problem in my math work.

    My job is to simplify/reduce the following exponentiation:
    4^(x+1)x-1

    My solution for it is following:

    4^(x+1)x-1​ = 4^(x+1)(x-1) = 4^x2-1

    But I got a feeling, that it's wrong. So I want to know, what I'm doing wrong.

    Thanks.
    First there is the matter of notation. Please note that \left ( 2^3 \right ) ^4 is not the same as 2^{(3^4)}

    I will presume that the problem is 4^{(x + 1) ^{x - 1}}

    So looking only at the exponent we have
    (x + 1)^{x - 1} = (x + 1)^x \cdot (x + 1)^{-1}

    If you need more, let us know.

    I'm rather curious about this. I can see no way to put the original expression into something that it can be reduced to.

    -Dan
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  5. #5
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    Re: Exponents for exponents

    I've tried working with the tip (thanks), and my current result is the following:

    4(x+1)^x * (x+1)^-1 = 41/x+1^(-x) * 1/x+1

    Again, am I not sure, if I'm doing it right. So it would be nice with a little more.
    Last edited by JrAl; September 24th 2012 at 11:18 AM.
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