$ \Bbb{Q}_p(ζ_{p^n})$ and $\Bbb{Q}_p(p^{1/n})$ are both totally ramified extension over $ \Bbb{Q}_p$ each has extension degree $p^n-p^{n-1}$ and $n$.
The former can be regarded as Lubin Tate extension, Frobenius power series $φ(X)＝(1＋X)^{p}-1$ gives the former Lubin Tate extension.
My question is, the latter does not come from Lubin Tate extension ? Does anyone know some relation between these two fields ?
Thank you in advance.