Question

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

Answer 1

`(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`