Answer
$a)$ $\Big(\dfrac{s^{2}t^{-4}}{5s^{-1}t}\Big)^{-2}=\dfrac{25t^{10}}{s^{6}}$
$b)$ $\Big(\dfrac{xy^{-2}z^{-3}}{x^{2}y^{3}z^{-4}}\Big)^{-3}=\dfrac{x^{3}y^{15}}{z^{3}}$
Work Step by Step
$a)$ $\Big(\dfrac{s^{2}t^{-4}}{5s^{-1}t}\Big)^{-2}$
$\Big(\dfrac{s^{2}t^{-4}}{5s^{-1}t}\Big)^{-2}=\Big(\dfrac{5s^{-1}t}{s^{2}t^{-4}}\Big)^{2}=\dfrac{25s^{-2}t^{2}}{s^{4}t^{-8}}=25s^{-2-4}t^{2-(-
8)}=...$
$...=25s^{-6}t^{10}=\dfrac{25t^{10}}{s^{6}}$
$b)$ $\Big(\dfrac{xy^{-2}z^{-3}}{x^{2}y^{3}z^{-4}}\Big)^{-3}$
$\Big(\dfrac{xy^{-2}z^{-3}}{x^{2}y^{3}z^{-4}}\Big)^{-3}=\Big(\dfrac{x^{2}y^{3}z^{-4}}{xy^{-2}z^{-3}}\Big)^{3}=\dfrac{x^{6}y^{9}z^{-12}}{x^{3}y^{-6}z^{-9}}=...$
$...=x^{6-3}y^{9-(-6)}z^{-12-(-9)}=x^{3}y^{15}z^{-3}=\dfrac{x^{3}y^{15}}{z^{3}}$
