Algebra-Picking numbers vs Algebra?

[chamb878]

I would greatly appreciate help with the following problem.
Thanks!

Q 1. If x and y are nonzero integers, is X^Y<Y^X?
1) x=y^2
2) y>2
What is the best and fastest way to do this question? I know there is a algebraic approach, but is their another way?

Thanks!

[RonPurewal]

per the forum rules, we need a citation of the original source of the problem. without a citation, we can't discuss it.

please provide the identity of the original source. thanks.