Exponents

For nonzero real numbers $a,b$ and integers $x,y$ :

$$a^0=1 (ab)^x=a^xb^x a^xa^y=a^{x+y}$$

$$\frac{a^x}{a^y}=a^{x-y} \bigg(\frac{a}{b}\bigg)^x = \frac{a^x}{b^x} a^{-x}=\frac{1}{a^x}$$