How do you simplify (3x^-1y^3)^2 / ((3xy^-1)^3 (9x^-9y^5))?

1 Answer
Ananda Dasgupta
Mar 22, 2018

(x^4y^4)/27

Explanation:

(3x^-1y^3)^2 / ((3xy^-1)^3 (9x^-9y^5)) = (3^2(x^-1)^2(y^3)^2)/((3^3x^3(y^-1)^3)(9x^-9y^5))
qquad =(3^2x^-2y^6)/((3^3x^3y^-3)(3^2x^-9y^5)) = (3^2x^-2y^6)/(3^(3+2)x^(3-9)y^(-3+5)) =(3^2x^-2y^6)/(3^5x^-6y^2) = 3^(2-5) x^(-2-(-6)) y^(6-2) = 3^-3x^4y^4=(x^4y^4)/27

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