nLab
Gelfond's theorem

If $a$ is an algebraic number different from $0$ or $1$, and $b$ irrational, then $a^b$ is transcendental (in particular irrational).

• A. O. Gelfond?, Transcendental and algebraic numbers, Dover Publications, New York 1960, translation from 1st Russian edition by Leo F. Boron.