Can an irrational number raised to an irrational power be rational?

If it can be rational, how can one prove it?

**Answer**

There is a classic example here. Consider A=√2√2. Then A is either rational or irrational. If it is irrational, then we have A√2=√22=2.

**Attribution***Source : Link , Question Author : John Hoffman , Answer Author : Pendronator*