Solution
= Solution
Regard $K$ as a <vector space> over $F$. Since $K$ is finite, a maximal <linearly independent> list has finite length $d$ and is a <basis>. Every element is uniquely a <linear combination> of its $d$ <basis vectors>, with $q$ choices for each coefficient. Hence $\boxed{|K|=q^d}$, with $d=[K:F]$. This includes $d=1$ when the extension is trivial.