Question

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

Answer 1

`-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^(-1/4)`. NOT `(-625)^(-1/4)`

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

`-625^(-1/4)`
`=-(1/625)^(1/4)`

I forgot the proof for this, I think it was the definition of radical numbers (?). It states that `a^(1/b)` is equal to `root(b)(a)`. Using this, we can then convert this to a number with a radical.

`-(1/625)^(1/4)`
`=-root(4)(1/625)`

Now look for the 4th root of `1/625`. The answer is `1/5`.

So your final answer is:
`-1/5`