Power Function is Completely Multiplicative

Theorem
Let $K$ be a field.

Let $z \in K$.

Let $f_z: K \to K$ be the mapping defined as:
 * $\forall x \in K: f_z \left({x}\right) = x^z$

Then $f_z$ is completely multiplicative.

Proof
Let $r, s \in K$.

Then: