Rational Exponents and Radicals

Consider the following two cases for any real number $a.$ $$\begin{array}{c}\sqrt[n]{a^n}=\{\begin{array}{l}a\text{ if }n\text{ is odd}\\ |a|\text{ if }n\text{ is even}\end{array}\end{array}$$ Because our radical has an even index and the variables have even exponents, we will need to use absolute value symbols to simplify our expression. Now, considering that $4$ is an even number, we can simplify the obtained expression. $$\begin{array}{c}\frac{\sqrt[4]{{\left(x^4\right)}^4}}{\sqrt[4]{2^4}\cdot \sqrt[4]{y^4}}\iff \frac{\left|x^4\right|}{|2|\cdot |y|}\end{array}$$ Finally, since the exponent of the numerator is even, it is always positive. Moreover, $2$ is also a positive number. This means we can remove the absolute value symbol from the numerator and from $2.$ $$\begin{array}{c}\frac{\left|x^4\right|}{|2|\cdot |y|}\iff \frac{x^4}{2|y|}\end{array}$$