  Let $\mathscr{R}$ be a prime ring of Char$(\mathscr{R}) \neq 2$ and $m\neq 1$
be a positive integer. If $S$ is a nonzero skew derivation with an associated
automorphism $\mathscr{T}$ of $\mathscr{R}$ such that $([S([a, b]), [a,
b]])^{m} = [S([a, b]), [a, b]]$ for all $a, b \in \mathscr{R}$, then
$\mathscr{R}$ is commutative.
