Question

How do you simplify `a^2(r^-3s)^-2`?

Answer 1

We know that `color(blue)((ab)^m = a^m*b^m`

Hence `a^2(r^-3s)^-2 = a^2 *(r^-3)^-2*s^-2`

We also know that `color(blue)((a^m)^n = a^(m*n)`

Hence `a^2 *(r^-3)^-2*s^-2 = a^2 * r^(-3*-2) * s^-2`

`= a^2*r^6*s^-2`

`color(blue)(a^-m = 1/a^m` (`a!=0`)

Hence `a^2*r^6*s^-2 = color(green)((a^2*r^6)/s^2`