###### 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 $$3\text{.}$$

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