Answer
$\frac{1}{x^{12}}$
Work Step by Step
$$\frac{(x^{-2}y)^{-3}}{(x^{2}y^{-1})^{3}}$$
When a product is raised to a power, raise each factor to that power.
$$=\frac{x^{(-2\times-3)}y^{-3}}{x^{(2\times3)}y^{(-1\times3)}}$$
$$=\frac{x^{6}y^{-3}}{x^{(6)}y^{(-3)}}$$
Regroup like terms then simplify
$$=(\frac{x^{-6}}{x^{6}})(\frac{y^{-3}}{y^{-3}})$$
Any number divided by itself equals one; and
When dividing exponential expressions with the same non-zero base, subtract the denominator's exponent from the numerator's exponent:
$$=x^{(-6-6)}\times1$$
$$=x^{-12}$$
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.
$$=\frac{1}{x^{12}}$$
