Powers and roots

$a^0 = 1$		 $a^1 = a$


$a^{-r} = 1/(a^r)$ 
$a^{1/n} = \sqrt[n]{a}$


$a^r a^s = a^{r+s}$		 
$a^r/a^s = a^{r-s}$


$a^s b^s = (ab)^s$ 
$a^s/b^s = (a/b)^s$


$(a^r)^s = a^{rs} = a^{sr} = (a^s)^r$ 

The following are special cases of the above:

$\sqrt[n]{a}/\sqrt[n]{b} = \sqrt[n]{a/b}$  
$a^{-(m/n)} = $\sqrt[n]{a}\sqrt[n]{b} = \sqrt[n]{ab}$\ $a^{m/n} = \sqrt[n]{a^m}...
...n]{b} = \sqrt[n]{a/b}$\ $a^{-(m/n)} = 1/(\sqrt[n]{a^m}) = 1/(\sqrt[n]{a})^m$\\$