16. \( (-x y)^{2} \cdot\left(2 x^{9} y^{5}\right)^{4} \)

To simplify the expression \( (-x y)^{2} \cdot\left(2 x^{9} y^{5}\right)^{4} \), we first handle each part separately. The first term can be expanded as \( (-1)^{2} x^{2} y^{2} = x^{2} y^{2} \) since squaring \(-1\) gives \(1\). For the second term, we apply the power of a product rule: \( (2^{4}) \cdot (x^{9})^{4} \cdot (y^{5})^{4} = 16 x^{36} y^{20} \). Now, multiplying these results together: \[ x^{2} y^{2} \cdot (16 x^{36} y^{20}) = 16 x^{2 + 36} y^{2 + 20} = 16 x^{38} y^{22}. \] Thus, the simplified expression is: \[ \boxed{16 x^{38} y^{22}}. \]