Simplify the given expression: $\frac{x^{45}}{y^{4}} \div-\frac{2 x^{9}}{y^{39}}$

Step 1 ：Rewrite the given expression: \(\frac{x^{45}}{y^{4}} \div -\frac{2 x^{9}}{y^{39}}\) as multiplication by flipping the second fraction: \(\frac{x^{45}}{y^{4}} \times -\frac{y^{39}}{2 x^{9}}\)

Step 2 ：Simplify the expression by using the properties of exponents: \(-\frac{x^{36}y^{35}}{2}\)

Step 3 ：Final Answer: The simplified expression is \(\boxed{-\frac{x^{36}y^{35}}{2}}\)