Answer
$n$ and $m$ are both even
Work Step by Step
$\textbf{Case 1}:$ $n$ odd
The expression $\sqrt[n]{x^m}$ is defined for any integer $m$ and any real $x$,
$\textbf{Case 2}:$ $n$ even
Case 2a: $m$ even
The expression $\sqrt[n]{x^m}$ is defined for any $m$ even and any real $x$ and we write:
$$\sqrt[n]{x^m}=|x|^{m/n}.$$
Case 2b: $m$ odd
The expression $\sqrt[n]{x^m}$ is defined for any $m$ odd and any positive $x$ and we write:
$$\sqrt[n]{x^m}=\sqrt[n]{x^{2k+1}}=x^{2k/n}\cdot \sqrt[n]x.$$
So the absolute value is needed when $n$ is even and $m$ is even.
