I have been using simple inequalities of fractional powers on a positive interval and keep abusing the inequality for $x>1$. I was just wondering if there is a nice way to prove the inequality in a couple line:
Let $x \in [1,\infty)$ and $r,s \in \mathbb{R}$
What is an easy way to prove the equality $r > s > 0$ implies $x^r > x^s$?