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