## anonymous 4 years ago Can rational to the power irrational be rational?

1. anonymous

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

2. anonymous

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

3. anonymous

(And 0)

4. anonymous

Are you sure no?

5. anonymous

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