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

1 Answer
Sep 19, 2015

Answer:

#-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#