For any real numbers $a$, $b$ and $c$, any rational numbers $k$ and $m$, and any positive integers $n$.
- $a^k\times a^m = a^{k+m}$
- $\dfrac{a^k}{a^m} = a^{k-m}$
- $(a^k)^m=(a^m)^k=a^{km}$
- $(ab)^m=a^mb^m$
- $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
- $a^{-1}=\dfrac{1}{a}$ for $a\neq0$
- $a^0=1$
- $\sqrt[n]{a} = a^\frac{1}{n}$ for $a\ge0$
- $\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$ for $a\ge 0$ and $b>0$
