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:

$$ $$ $$