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