(-2x^2y)^3*(5xy^3)^2

I will be happy to critique your work.

I think it is:
-200x^12y^19

The negative two hundred is right.

Notice this:
(x^a)^b = x^ab

Now redo the x and y powers, and you will have it.

I know the first one is 81 but what is the second one?

81? are you kidding?

(-2x^2y)^3 = -8 x^6 y^3