Answer
$4r^{8}$
Work Step by Step
We are given the expression $\frac{8r^{4}}{2r^{-4}}$.
To simplify, we can use the quotient rule, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$ (where a is a nonzero real number, and m and n are integers).
Therefore, $\frac{8r^{4}}{2r^{-4}}=\frac{8}{2}\times r^{4-(-4)}=4\times r^{4+4}=4r^{8}$.