Question

How do you simplify `(6x^2y)^2/((2x^4)(xy^2))`?

Answer 1

`((6x^2y)^2)/((2x^4)(xy)^2)= color(green)(18/x)`

Explanation:

`((6x^2y)^2)/((2x^4)(xy)^2)`

`color(white)("XXX")=(36x^4y^2)/(2x^4)(xy^2)`

`color(white)("XXX")=(cancel(36)^18x^4y^2)/((cancel(2)x^4)(xy^2))`

`color(white)("XXX")=(18cancel(x^4)y^2)/((cancel(x^4))(xy^2))`

`color(white)("XXX")=(18cancel(y^2))/(xcancel(y^2))`

`color(white)("XXX")=18/x`

Answer 2

`= 18/x`

Explanation:

Start by getting rid of the brackets ... I prefer to work with the numerator and denominator separately first.

`((6x^2y)^2)/[(2x^4)(xy^2)] = (36x^4y^2)/(2x^5y^2)`

`= 18/x`

Subtract the indices of like bases.