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Math Help - Simplifying exponents.

  1. #1
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    Simplifying exponents.

    Hello, I'm not too sure how the exponents ended up as (1 / 1- a - b) in the last line of the equation. Any help would be great!! thank you!!
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    Last edited by mr fantastic; October 8th 2011 at 11:11 PM. Reason: Re-titled.
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  2. #2
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    Re: Simplifying exponents.

    Quote Originally Posted by abstraktz View Post
    Hello, I'm not too sure how the exponents ended up as (1 / 1- a - b) in the last line of the equation. Any help would be great!! thank you!!
    1.

    a^r=v~\implies~a=v^{\frac1r}

    2.
    \left(\frac{Y_1}{L_i}\right)^* = \frac{\left(s_i^k\right)^\alpha \left(s^H\right)^\beta}{\delta^{\alpha + \beta}} \cdot \left( \left(\frac{Y_1}{L_i}\right)^* \right)^{\alpha+\beta}

    Divide this equation by \left(\left(\frac{Y_1}{L_i}\right)^*\right)^{ \alpha +\beta}
    which yields:

    \left(\left(\frac{Y_1}{L_i}\right)^*\right)^{1-\alpha-\beta} = \frac{\left(s_i^k\right)^\alpha \left(s^H\right)^\beta}{\delta^{\alpha + \beta}}

    3. Now calculate \left(\frac{Y_1}{L_i}\right)^* as shown in step #1.
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  3. #3
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    Re: Simplifying exponents.

    Thank you !!!
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