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

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=22. Then A is either rational or irrational. If it is irrational, then we have A2=22=2.

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

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