Answer
$a)$ $16x^{3}$
$b)$ $r^{10}s^{2}$
Work Step by Step
$a)$ $\dfrac{x^{2}(2x)^{4}}{x^{3}}$
Evaluate the power in the numerator:
$\dfrac{x^{2}(2x)^{4}}{x^{3}}=\dfrac{x^{2}(16x^{4})}{x^{3}}=...$
Evaluate the product in the numerator:
$...=\dfrac{16x^{6}}{x^{3}}=...$
Evaluate the division and simplify:
$...=16x^{6-3}=16x^{3}$
$b)$ $\Big(\dfrac{r^{2}s^{4/3}}{r^{1/3}s}\Big)^{6}$
Evaluate the power:
$\Big(\dfrac{r^{2}s^{4/3}}{r^{1/3}s}\Big)^{6}=\dfrac{r^{12}s^{8}}{r^{2}s^{6}}=...$
Evaluate the division and simplify:
$...=r^{12-2}s^{8-6}=r^{10}s^{2}$