# How do you simplify 2^-4?

##### 1 Answer
Jun 29, 2016

${2}^{- 4} = \frac{1}{16}$

#### Explanation:

As ${a}^{m} \div {a}^{n} = {a}^{m - n}$, if $m = 0$,

we have ${a}^{0} \div {a}^{n} = {a}^{0 - n}$

or $\frac{1}{a} ^ n = {a}^{- n}$ i.e. ${a}^{- n} = \frac{1}{a} ^ n$

Hence, ${2}^{- 4} = \frac{1}{2} ^ 4 = \frac{1}{2 \times 2 \times 2 \times 2} = \frac{1}{16}$