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e^(i theta) = cos theta + i sin theta (Euler's identity) thus e^(i pi) = cos pi + i sin pi = -1 + i(0) = -1
We know that e and i pi are irrational (in fact i pi isn't even a real) and -1 is rational.
Therefore there exist two numbers a and b such that both a and b are irrational but a^b is rational.
In fact log of just about anything is irrational so e^(log x) works as well for just about all rational x, but Euler's identity is cool so I wanted to use that.
[1] https://www.justice.gov/atr/mission