Answer
$-4r^{6}$
Work Step by Step
According to the power rule for exponents, $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are integers and $a$ is a real number).
Therefore, $-4r^{-2}(r^{4})^{2}=-4r^{-2}r^{4\times2}=-4r^{-2}r^{8}$.
According to the product rule for exponents, $a^{m}\times a^{n}=a^{m+n}$.
Therefore, $-4r^{-2}r^{8}=-4r^{-2+8}=-4r^{6}$.
