If x and y are distinct positive integers, what is the value

I think it's worth remembering that \(4^2=16=2^4\), I've seen several GMAT questions on number properties using this (another useful property \(8^2=4^3=2^6=64\)).

But if you don't know this property:

Given: \(x^y = y^x\) and \(x>y\), also \(x\) and \(y\) are distinct positive integers.
Couple of things:
\(x\) and \(y\) must be either distinct positive odd integers or distinct positive even integers (as odd in ANY positive integer power is odd and even in ANY positive integer power is even).

After testing several options you'll see that \(x=4\) and \(y=2\) is the only possible scenario: because, when \(y\geq{2}\) and \(x>{4}\), then \(x^y\) (bigger value in smaller power) will be always less than \(y^x\) (smaller value in bigger power): \(5^3<3^5\), or \(6^2<2^6\), or \(8^2<2^8\), or \(10^2<2^{10}\), ....