Is it true that every element $x \in \mathcal{O}_{\overline{\mathbb{Q}}_p}$ can be written as $x=u \cdot p^{m/p^s}$ where $u$ is a unit, $m \in \mathbb{N}$ and $s \in \mathbb{N}$?
Note that $p$ is a uniformizer of $\mathbb{Z}_p$, every element $x \in \mathbb{Z}_p$ can be written as $x= u \cdot p^m$ with $u$ is a unit of $\mathbb{Z}_p$. My question is whether every element in the ring of integers of the algebraic closure $\overline{\mathbb{Q}}_p$ can be expressed in term of some $p$-power root of $p$?