A Power Raised Again

When a power is raised to another power, you multiply the exponents. The rule is called the power of a power rule.

In $\left(x^{3}\right)^{2}$, the base of the outer power is $x^{3}$. Squaring $x^{3}$ means multiplying it by itself: $x^{3}x^{3}$. Each copy of $x^{3}$ holds three factors of $x$, so there are six factors of $x$ in total, and $\left(x^{3}\right)^{2} = x^{6}$.

The example shows why the exponents multiply. There are three factors of $x$ in each copy, and there are two copies, so there are $3\cdot 2 = 6$ factors in all.

The parentheses make the whole inner power $x^{3}$ the base of the outer power. Both exponents count factors of $x$, so both are used when you simplify.