Question

Can rational to the power irrational be rational?

Answer 1

No, but I have no formal proof of it, if I can come up with one, I'll post it up.

Answer 2

(Other than the trivial case: \(1^a\), where \(a\in \mathbb{R}\))

Answer 3

(And 0)

Answer 4

Are you sure no?

Answer 5

I'm pretty sure, yes, but you can try proving it yourself, it doesn't look to be a simple, elementary proof.