Rules of Exponents

1. $x^{m} · x^{n} = x^{m + n}$

2. $( \frac { x ^ { m } } { x ^ { n } } )= x^{m − n}$

3. $\left(x^{m} \right) ^{n} = x^{mn}$

4. $\left(xy\right) ^{m} = x^{m}y^{m}$

5. $( \frac { x } { y } ) ^ { n } = \frac { x ^ { n } } { y ^ { n } }$

Rules 1, 2, and 3 are the most commonly used, but rules 4 and 5 are also useful.