Question

How do you simplify `((r^-1s^2t^-3)/(r^-2s^0t^1))^-1`?

Answer 1

`r^-1s^-2 t^4` or `t^4/(rs^2)`

Explanation:

First, using the rules for exponents you can eliminate the denominator of this problem as follows:

`((r^-1s^2t^-3)/(r^-2s^0t^1))^-1 -> (r^(-1 - -2) s^(2 - 0)t^(-3 - 1))^-1 ->`

`(r^(-1 + 2) s^2t^-4)^-1 -> (r^1s^2t^-4)^-1`

Now that we have simplified the fraction we can apply the exponent to the entire term continuing to use the rules for exponents:

`(r^1s^2t^-4)^-1 -> r^(1*-1)s^(2*-1)t^(-4*-1) -> r^-1s^-2 t^4` or

`t^4/(r^1s^2) -> t^4/(rs^2)`