# How do you simplify 4/m^ -7?

Mar 27, 2016

$\frac{4}{m} ^ \left(- 7\right) = 4 {m}^{7}$ with exclusion $m \ne 0$

#### Explanation:

If $m \ne 0$ then:

${m}^{- 7} = \frac{1}{\underbrace{m \times m \times . . \times m}} _ \text{7 times} = \frac{1}{m} ^ 7$

So:

$\frac{4}{m} ^ \left(- 7\right) = \frac{4}{\frac{1}{m} ^ 7} = 4 {m}^{7}$

Note that if $m = 0$ then the left hand side is undefined, but the right hand side is defined, so $m = 0$ is an excluded value.