How do you simplify #-5^-3#?

1 Answer
Oct 29, 2015

Answer:

#-5^-3=-1/125#

Explanation:

In the expression #-5^-3# there are 2 operations: power and multiplication by #(-1)#. According to the order of operations we have to calculate the power first remembering, that if the exponent is negative we have to write the expression as a positive power of the reciprocal of the base:

#(a/b)^-c=(b/a)^c#

So we get: #[-(1/5^3)]#
Finally we can calculate the power #5^3# and write the final answer:

#-5^-3=-(1/5^3)=-1/125#