If a set $\Sigma$ of alphabets is of cardinality $k$, does $\Sigma^n$ have cardinality of $k^n$?

Question

As title says, if a set $\Sigma$ of alphabets is of cardinality $k$, does $\Sigma^n$ have cardinality of $k^n$? This seems to be the case because for each character of the string of length $n$, you have $k$ choices, so $k^n$. Is this right?

Answer 1

For any set $S$ of cardinality $k$, $S^n$ has cardinality $k^n$. This is fundamental property of Cartesian product