# GCD and LCM of powers in GCD domains

Let $$R$$ be a GCD domain. This means that it is an integral domain in which any 2 elements have a GCD, and hence also an LCM.

Question:

Is it true that if $$z$$ is a GCD or LCM of $$x$$ and $$y$$ in $$R$$, then $$z^n$$ is a GCD or LCM of $$x^n$$ and $$y^n$$ for any nonnegative integer $$n$$?

Remember that GCDs and LCMs are only defined up to associates.