### Home > PC > Chapter 1 > Lesson 1.1.2 > Problem1-28

1-28.

Simplify each expression using the rules of exponents.

1. $\left(5a^{−2}\right)^{2}$

1. $\left(m^{−1}n^{−2}\right)^{3}$

1. $\left(2x^{−1}\right)^{2} \left(2x^{0}\right)$

### 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.