Question

How do you simplify `(2r^-4s^2)^-3` and write it using only positive exponents?

Answer 1

`r^12/(8s^6)`

Explanation:

`x^-a=1/x^a` and vice versa.

Therefore: `r^-4=1/r^4` and `(2r^-4s^2)^-3=1/(2r^-4s^2)^3`

`(2r^-4s^2)^-3=1/(2r^-4s^2)^3=1/(2(1/r^4)s^2)^3`

which is:

`=1/((2s^2)/r^4)^3`

This is = `1/((8s^6)/r^12)` which is = `r^12/(8s^6)`