Solution
= Solution
Regard $K$ as a <vector space> over its <prime field>[prime subfield] $\mathbb F_p$. Since $K$ is finite, a maximal <linearly independent> list terminates and is a finite <basis>, of some dimension $n\geq1$. Each <field> element has a unique coordinate vector in $\mathbb F_p^n$, so
$$
\boxed{|K|=p^n}.
$$