$-(\frac{2}{3}x^2y^2)^4 * (-2\frac{1}{4}xy^3)^3 = -\frac{16}{81}x^8y^8 * (-\frac{9}{4}xy^3)^3 = -\frac{16}{81}x^8y^8 * (-\frac{729}{64}x^3y^9) = \frac{9}{4}x^{11}y^{17} = 2\frac{1}{4}x^{11}y^{17}$