Question

Can a rational number (not including 0, 1, or -1) be raised to an irrational power be rational?

Answer 1

I think I have asked this question sometime back
\[(a/b)^x = p/q \iff x = \log_{a/b} (p/q) \]

Answer 2

There exist irrational numbers that are logarithm of a rational number relative to a rational number base. So we're done.

Answer 3

Awesome thanks that makes a lot of sense!