\(\left(\frac{8xy}{9y}\right)^{-\frac{1}{2}}=\left(\frac{9y}{8xz}\right)^\frac{1}{2}=\frac{\sqrt{9y}}{\sqrt{8xz}}=\frac{3\sqrt{y}}{\sqrt{4\cdot2xz}}=\frac{3\sqrt{y}}{2\sqrt{2xz}}\cdot\frac{\sqrt{2xz}}{\sqrt{2xz}}=\frac{3\sqrt{2xyz}}{2\cdot2xz}=\frac{3\sqrt{2xyz}}{4xz}\)
