How do you simplify #((3x^-2 y^3 )/(2xy))^-2#?

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Answer 1 · 2015-10-11T00:08:43

#(4x^6)/(9y^4)#

Try to simply the expression

#(3x^(-2)y^3)/(2xy)#

first, then worry about the #-2# exponent.

Notice that you can write

#(3x^(-2)y^3)/(2xy) = (3 * y^3)/(2xy) * 1/x^2 = (3y^2)/(2x^3)#

The original expression now becomes

#((3y^2)/(2x^3))^(-2) = ((2x^3)/(3y^2))^2 = (2^2 * x^(3 * 2))/(3^2 * y^(2 * 2)) = color(green)((4x^6)/(9y^4))#