How do you simplify (\frac { x ^ { - 3} x ^ { 2} } { x ^ { 3} x ^ { - 2} } ) ^ { 2}?

1 Answer
Mar 10, 2018

The answer is 1/x^4 or x^-4.

Explanation:

You have to use these exponent rules:

(1)qquadqquadx^m+x^n=x^(m+n)

(2)qquadqquadx^-m=1/x^m

(3)qquadqquad(x^m)^n=x^(m*n)

(4)qquadqquad(x/y)^m=x^m/y^m

Now here's the actual problem:

color(white)= ((x^-3x^2)/(x^3x^-2))^2

= ((x^-3*x^2)/(x^3*x^-2))^2

= (color(blue)(x^-3*x^2)/color(red)(x^3*x^-2))^2

= (color(blue)(x^-1)/color(red)(x^1))^2

= (1/(color(blue)(x^1)*color(red)(x^1)))^2

= (1/color(purple)(x^2))^2

= 1^2/((color(purple)(x^2))^2)

= 1/x^4

= x^-4