Is there a "one-line" proof of $x<y\Rightarrow x^n<y^n$ (for $n$ an odd natural number)?
$f(t)=t^{2k+1}$ is a strictly monotonic function, as $f'(t)>0$ (except at $t=0$).
$f(t)=t^{2k+1}$ is a strictly monotonic function, as $f'(t)>0$ (except at $t=0$).