If GCD(a,b)=d then GCD(a^n,b^n)=d^n?

Question

If GCD(a,b)=d,

then can we say that GCD(a^n,b^n)=d^n? for all positive integers n.

This doubt is inspired from GCD(a,b)=1 implies GCD(a^n,b^n)=1 for all positive integers n.