Power Function Preserves Ordering in Ordered Semigroup

Theorem
Let $\struct {S, \circ, \preceq}$ be an ordered semigroup.

Let $x, y \in S$ such that $x \preceq y$.

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

Then:
 * $x^n \preceq y^n$

where $x^n$ is the $n$th power of $x$.