Example2.7.4

Simplify \(\left(x^2\right)^3\text{.}\)

To simplify \(\left(x^2\right)^3\text{,}\) we write this out in its expanded form, as a product of \(x\)'s, we have

\begin{align*} \left(x^2\right)^3 \amp=\left(x^2\right) \cdot \left(x^2\right)\cdot\left(x^2\right)\\ \amp=(x \cdot x)\cdot (x \cdot x)\cdot (x \cdot x)\\ \amp=x^6 \end{align*}

Note that we obtained the exponent of \(6\) by multiplying \(2\) and \(3\text{.}\)

in-context