Answer
$\frac{x^{4}}{4y^{8}}$
Work Step by Step
The given expression is
$=(\frac{2x^0}{4x^{-2}y^4})^2$
$=(\frac{2x^0}{2^2x^{-2}y^4})^2$
Use $\frac{a^n}{a^m}=a^{n-m}$.
$=(\frac{x^{0+2}}{2^{2-1}y^4})^2$
Simplify.
$=(\frac{x^{2}}{2^{1}y^4})^2$
Use $(\frac{a}{b})^n=\frac{a^n}{b^n}$.
$=\frac{(x^2)^2}{(2y^4)^2}$
Use $(ab)^n=a^nb^n$.
$=\frac{(x^2)^2}{(2)^2(y^4)^2}$
Use $(a^n)^m=a^{n\cdot m} $
$=\frac{x^{2\cdot 2}}{2^{ 2}y^{4\cdot 2}}$
Simplify.
$=\frac{x^{4}}{2^{2}y^{8}}$
$=\frac{x^{4}}{4y^{8}}$.
