Question

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

Answer 1

`-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`