Answer
$\Big(\dfrac{r^{-2}s^{-3}}{r^{-4}s^{-3}}\Big)^{-3}=\dfrac{1}{r^{6}}$
Work Step by Step
$\Big(\dfrac{r^{-2}s^{-3}}{r^{-4}s^{-3}}\Big)^{-3}$
Evaluate the exponential expression:
$\Big(\dfrac{r^{-2}s^{-3}}{r^{-4}s^{-3}}\Big)^{-3}=\dfrac{r^{6}s^{9}}{r^{12}s^{9}}=...$
Evaluate the division and simplify:
$...=r^{6-12}s^{9-9}=r^{-6}s^{0}=r^{-6}=\dfrac{1}{r^{6}}$