###### Example2.7.6

Simplify $$(xy)^5\text{.}$$

To simplify $$(xy)^5\text{,}$$ we write this out in its expanded form, as a product of $$x$$'s and $$y$$'s, we have

\begin{align*} (xy)^5 \amp=(x \cdot y) \cdot (x \cdot y) \cdot (x \cdot y) \cdot (x \cdot y) \cdot (x \cdot y)\\ \amp=(x \cdot x \cdot x \cdot x \cdot x) \cdot (y \cdot y \cdot y \cdot y \cdot y)\\ \amp=x^5 y^5 \end{align*}

Note that the exponent on $$xy$$ can simply be applied to both $$x$$ and $$y\text{.}$$

in-context