  A bounded linear operator $A$ on a Hilbert space $\mathcal{H}$ is posinormal
if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. We show
that if $A$ is posinormal with closed range, then $A^n$ is posinormal and has
closed range for all integers $n\ge 1$. Because the collection of posinormal
operators includes all hyponormal operators, we obtain as a corollary that
powers of closed-range hyponormal operators continue to have closed range. We
also present a simple example of a closed-range operator $T: \mathcal{H}\to
\mathcal{H}$ such that $T^2$ does not have closed range.
