Answer
$\dfrac{y^4}{x^{8}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(x^4y^{-2})^{-2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^{4(-2)}y^{-2(-2)}
\\\\=
x^{-8}y^{4}
\\\\=
\dfrac{y^4}{x^{8}}
.\end{array}
For more complicated problems, it is helpful to remember that you can flip the location of numbers with negative exponents. In other words, you can move numbers with a negative exponent that are in the numerator to the denominator, and you can move numbers with a negative exponent in the denominator to the numerator.
