1. ## 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!!

2. ## Re: Simplifying exponents.

Originally Posted by abstraktz
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.

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

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

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

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

3. Now calculate $\displaystyle \left(\frac{Y_1}{L_i}\right)^*$ as shown in step #1.

3. ## Re: Simplifying exponents.

Thank you !!!