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

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Answer 1 · 2018-03-10T01:05:27

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

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 #