### Home > PC > Chapter 1 > Lesson 1.1.2 > Problem1-26

1-26.

Simplify using the rules of exponents. Or state why it cannot be simplified.

### 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.

1. $a^{b} · a^{c}$

$a^{b+c}$

1. $a^{−b}· a^{c}$

$a^{(c-b)}$

1. $a^{b} + a^{c}$

Can't be simplified. We are not multiplying.

1. $a · a^{b}$

$a^{b+1}$

1. $a^{0} · a^{b}$

$a^b$

1. $a^{(b + c)} · a^{2c}$

$a^{(3c+b)}$