1. The work is fine.

2. There is one error that messed up your answer.

(3)2 (x-2)2 (y2)2

-12 x3 y-3

In this, you simplified it to:

3x4 y4

-12 x3 y-3

Which is wrong, when you separate each component of the first part I copied, you end up getting the following on the numerator:

(3)^2 = 9

(x^-2)^2 = (x^-2)*(x^-2) = (x^(-2 + -2)) = (x^-4)

(y^2)^2 = (y^2)*(y^2) = y^4

The numerator is as such:

9x^-4*y^4

The whole fraction is:

9x^-4*y^4

-----------

-12x^3*y^-3

Now we have to use the law of inverses, which states that:

x^-1 = 1/x^1

So:

x^-4 = 1/x^4

And:

1/y^-3 = y^3

Now we have to rearrange the fraction:

9y^4*y^3

----------

-12x^3*x^4

Therefore, we have:

3y^7

-----

-4x^7