Answer
$\dfrac{r^{58}}{16s^{14}}$
Work Step by Step
$\dfrac{(r^7s^{-5})^6}{(2r^{-4}s^{-4})^4}=\dfrac{(r^{7*6}s^{-5*6})}{(2^4r^{-4*4}s^{-4*4})}=\dfrac{(r^{42}s^{-30})}{(16r^{-16}s^{-16})}=\dfrac{(r^{42}r^{16}s^{16})}{(16s^{30})}=\dfrac{r^{(42+16)}s^{(16-30)}}{16}=\frac{1}{16}r^{58}s^{-14}=\dfrac{r^{58}}{16s^{14}}$
