## Intermediate Algebra (12th Edition)

$|x^{5}|$
We know that $\sqrt[6] x^{30}=|x^{5}|$, because $(x^{5})^{6}=x^{5\times6}=x^{30}$. Since $x$ is being raised to an odd positive power, we must use an absolute value sign to guarantee that the result is not negative (because $x^{5}$ is negative when $x$ is negative, and we know that there is no real number solution to $\sqrt[n] a$ when $a$ is negative and $n$ is even).