Right-distributive


Definition

\(*\) is right-distributive over \(+\) if and only if

$$\forall x,y,z \in S : (y + z) * x = (y * x) + (z * x)$$
THEOREM   

Exponentiation is right-distributive over multiplication.

$$\forall x,y,z \in \mathbb{N} : (xy)^z = x^zy^z$$

Proof available