Show prove in detail why (xyz) to the n power equal x to the n power y to the n power and z to the n power

Example if n=2 (xyz)^2=(xyz)(xyz)=xxyyzz=x^2y^2z^2 if n=4 (xyz)^4=(xyz)(xyz)(xyz)(xyz)==x^4y^4z^4 the reason is that multiplication is associative (can move parenthasees around with multiply or add)