1.(-5x^-3y^-1)^2/(2xy^2)^-3
=(25x^-6y^-2)*(2xy^2)^3
=(25x^-6y^-2)*(8x^3y^6)
=200x^-3y^4
2.(a^-3)^-2/[a^3b*(a^-1b)^-2]
=(a^6)/[a^3b*(a^2b^-2)]
=(a^6)/[a^5b^-1]
=a/ b^-1
=ab
3.(2x^-2y^-1)^2*(3xy^2)^3/(3x^-1y^3)^-2
=(4x^-4y^-2)*(27x^3y^6)*(3x^-1y^3)^2
=(4x^-4y^-2)*(27x^3y^6)*(9x^-2y^6)
=972x^-3y^10