For the problem $\displaystyle (3/(5-x))^5$ Do you FOIL the bottom, or do you distribute the exponent?
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$\displaystyle \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ If you really needed to expand the denominator, then use the bionomial theorem: $\displaystyle (x+y)^n = \sum^{n}_{k=0}\left( \begin{array}{c} {n} \\ {k}\end{array}\right) x^{n-k}y^k$
$\displaystyle \bigg(\frac{3}{5-x}\bigg)^5$ You would foil out the bottom $\displaystyle \frac{243}{(5-x)^5}$ But the fastest way would be binomial theorem
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