# How do you simplify the expression -625^(- 1/4)?

Sep 19, 2015

$- \frac{1}{5}$

#### Explanation:

Just to be sure, I want to point out that the negative symbol is not enclosed in a parenthesis with 625 which means that we are looking for the negative of ${625}^{- \frac{1}{4}}$. NOT ${\left(- 625\right)}^{- \frac{1}{4}}$

First things first, there is a negative sign in the exponent. We can remove that by getting the reciprocal of 625.

$- {625}^{- \frac{1}{4}}$
$= - {\left(\frac{1}{625}\right)}^{\frac{1}{4}}$

I forgot the proof for this, I think it was the definition of radical numbers (?). It states that ${a}^{\frac{1}{b}}$ is equal to $\sqrt[b]{a}$. Using this, we can then convert this to a number with a radical.

$- {\left(\frac{1}{625}\right)}^{\frac{1}{4}}$
$= - \sqrt[4]{\frac{1}{625}}$

Now look for the 4th root of $\frac{1}{625}$. The answer is $\frac{1}{5}$.

$- \frac{1}{5}$