Answer
$\frac{y^{7}}{x^{8}}$
Work Step by Step
$\frac{(xy^{-2})^{-2}}{(x^{-2}y)^{-3}}$
When a product is raised to a power, raise each factor to that power.
= $\frac{(x^{1\times-2}y^{-2\times-2})}{(x^{-2\times-3}y^{1\times-3})}$
= $\frac{x^{-2}y^{4}}{x^{6}y^{-3}}$
When dividing exponential expressions with the same non-zero base, subtract the denominator's exponent from the numerator's exponent:
= $x^{-2}$$\times$$x^{-6}$$\times$$y^{4}$$\times$$y^{3}$
=$x^{-2-6}$$y^{4+3}$
=$x^{-8}$$y^{7}$
When an exponent is negative, write the expression as a fraction and switch the position of the base from the numerator to the denominator (or vise versa) and make the exponent positive.
=$\frac{y^{7}}{x^{8}}$
