  Let $\alpha, \beta$ be two relatively prime algebraic integers in a number
field $K$ and $N$ be a positive integer. We show that the number of
$n\in\{1,2,\dots,N\}$ such that the $\beta$-adic expansion of $\alpha^n$ omits
a given digit is less than $C_1 N^{\sigma(\beta)}$, where
$\sigma(\beta):=\frac{\log(|N(\beta)|-1)}{\log|N(\beta)|}$ and $C_1$ is an
absolute constant, if all prime ideal factors of $\beta$ are unramified and
their norms are integer primes.
