1. ## Question on exponents

For the problem $(3/(5-x))^5$ Do you FOIL the bottom, or do you distribute the exponent?

2. $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$

If you really needed to expand the denominator, then use the bionomial theorem:
$(x+y)^n = \sum^{n}_{k=0}\left( \begin{array}{c} {n} \\ {k}\end{array}\right) x^{n-k}y^k$

3. $\bigg(\frac{3}{5-x}\bigg)^5$

You would foil out the bottom

$\frac{243}{(5-x)^5}$

But the fastest way would be binomial theorem