Multiplication of powers:

$$a^m·a^n=a^{m+n}$$

Division of powers:

$$\frac{a^m}{a^n}=a^{m-n}$$

Changing a negative power exponent to a positive one:

$${\left(\frac{a}{b}\right)}^{-n}={\left(\frac{b}{a}\right)}^n$$

$$a^{-n}=\frac{1}{a^n}$$

Converting division of fractions to multiplication:

$$\frac{a}{b}:\frac{c}{d}=\frac{a}{b}·\frac{d}{c}$$