$b^{a^{1/n}}$: is it an irrational number?

Question

A power type $b^{a^{1/n}}$ where $b$, $a$ and $n$ are positive integers greater than $1$ and $a^{1/n}$ is irrational, always represents an irrational number?

Answer 1

Yes, it is in fact transcendental by the Gelfond-Schneider theorem.