Power Function is Strictly Increasing on Positive Elements

Theorem
Let $\left({R, +, \circ, \le}\right)$ be an ordered ring.

Let $x, y \in R$.

Let $n \in \N_{>0}$ be a strictly positive integer.

Let $0 < x < y$.

Then:
 * $0 < \circ^n \left({x}\right) < \circ^n \left({y}\right)$

Proof
The result follows by repeated application of Multiplying Positive Inequalities.

Also see

 * Odd Power Function is Strictly Increasing