Let $m$ and $n$ be positive integers and let $a$ represent a real number, a variable, or an algebraic expression. 1. $$\frac{{{a^m}}}{{{a^n}}} = {a^{m – n}}$$, $$m > n$$, $$a \ne 0$$. 2. $$\frac{{{a^n}}}{{{a^n}}} = 1 = {a^0}$$, $$a \ne 0$$.