How do you simplify #\frac { 2x ^ { 2} \cdot 3y ^ { 2} } { 3x ^ { 3} y ^ { 3} }#?

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Answer 1 · 2016-10-17T04:12:15

The answer is #color(blue)(2/(xy)#.

Simplify: #(2x^(2)3y^2)/(3x^3y^3)#

Simplify the numerator.

#(6x^2y^2)/(3x^(3)y^3)#

Apply the exponent quotient rule: #a^m/a^n=a^(m-n)#.

#(6x^(2-3)y^(2-3))/3=#

#(6x^(-1)y^(-1))/3#

Simplify #6/3# to #2#.

#(cancel(6)x^(-1)y^(-1))/cancel(3)=#

#2x^(-1)y^(-1)#

Apply negative exponent rule: #a^(-m)=1/a^m#.

#2/(xy)#