How do I write $\omega_1^{\omega}$ in a Cantor Normal form?

Question

I would like to ask about an example.

Write an ordinal in a Cantor Normal form: $\omega_1^{\omega}$. The problem is, that I absolutely don't know how to apply a theory on this example. I have not found any materials which would explain some examples. I would be pleased if somebody try to explain it me here. Thank you very much.

Answer 1

Thank you for your advice and comments I thing that I am a little bit cleverer now. If for every ordinal number $\omega_n$, bigger than $\epsilon_0$, pays: $\omega^{\omega_n} = \omega_n$ and $\omega_1^{\omega}$ is bigger than $\epsilon_0$, does it mean, that $\omega_1^{\omega}$ is in the Cantor form written as $\omega^{\omega_1^{\omega}}$?

Thanks