## siddhantsharan 2 years ago Can rational to the power irrational be rational?

1. LolWolf

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

2. LolWolf

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

3. LolWolf

(And 0)

4. siddhantsharan

Are you sure no?

5. LolWolf

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