Let c>1 and $\displaystyle m,n \in N \mbox { with } \ m>n : \\\\\\\\\\\mbox {prove that} \ {c^m}> {c^n}$
$\displaystyle c^{m-n}>1$ so we can then proceed in the following way
$\displaystyle c^{m}c^{-n}c^{n}>1c^{n}$
$\displaystyle c^{m}>c^{n}$