Answer :

[tex]\left(\frac{(x^4y^{-2})^4}{(2x^2)^2\cdot2x^0y^3}\right)^2=\\ \left(\frac{x^{16}y^{-8}}{4x^4\cdot2y^3}\right)^2=\\ \left(\frac{x^{16}y^{-8}}{8x^4y^3}\right)^2=\\ \left(\frac{x^{12}y^{-11}}{8}\right)^2=\\ \frac{x^{24}y^{-22}}{64}[/tex]