Let $K / F$ and $L / K$ be finite field extensions. Then $$ \begin{align*} &\# \{ F\text{-embeddings }\phi : L \to \overline{F} \} \\ =&\# \{ F\text{-embeddings }\varphi : K \to \overline{F} \} \cdot \# \{ K\text{-embeddings }\varphi : L \to \overline{K} \}. \end{align*} $$