x^-1y^0 do you do 1/x*1=1/x and how do you do x^-2y^1\ x^1y^2 ?

yes, x^-1 y^0 = 1/x

and, as you know, dividing means subtracting exponents, so

(x^-2 y^1)/(x^1 y^2)
= x^(-2-1) y^(1-2) = x^-3 y^-1 = 1/(x^3 y)