Hey, this question is simple enough, I know the answer. But I need a justification for it.

As x -> infinity, f(x) = xa^x -> 0. ( if 0 < a < 1)

I can justify that a^x goes to 0 when x goes to infinity, but that other x term is making it a little more complicated to justify. Do i just say that a^x is getting smaller at a rate faster than x is increasing?