If $a \in \mathbb{A}$\{$\mathbb{0,1}$}, $b \in \mathbb{A}$\ $\mathbb{Q}$ then $a^b$ is transcedental.

Question

For my math study, I have to prove the following:

Let's denote the set of algebraic numbers with $\mathbb{A}$.

Prove:

If $a \in \mathbb{A}$\{$\mathbb{0,1}$}, $b \in \mathbb{A}$\ $\mathbb{Q}$ then $a^b$ is transcedental.

I'm trying to use Baker's theorem to proof this, but I don't know how to apply it. Could you help me with that?

Thanks in advance!