How do you simplify #( -z^3 z^-6)/(-3z^2 )#?
There are several laws of indices in this expression, it does not matter which you regard as being the most important. You can apply any of the laws in any order.
Note: a negative sign in front is not the same as a negative sign in the index
"add and subtract indices"
Or: "a negative index indicates a reciprocal"