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

1 Answer
Dec 4, 2016

Answer:

#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)#