How do I find the following?
$\displaystyle \prod a(1-x_{i})^{a-1}$?
I assume it's $\displaystyle a^n$ multiplied by something. I can't figure out how to express the product of the $\displaystyle (1-x_{i})^{a-1}$ part.
Is the problem to "simplify" $\displaystyle \prod\limits_{i=1}^n a(1-x_{i})^{a-1}$? If so, not much can be done: since the $\displaystyle x_i$ dependence on the product index $\displaystyle i$ is not known. But maybe you are already happy with something like this
$\displaystyle \prod\limits_{i=1}^n a(1-x_{i})^{a-1}=a^n \left(\prod\limits_{i=1}^n(1-x_i)\right)^{a-1}$