Example 2.9.6

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 \(y\text{.}\)

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