Simplify. \[ \left(\frac{-3 x}{y^{3}}\right)^{4} \] Write your answer without parentheses.

To simplify the expression \(\left(\frac{-3 x}{y^{3}}\right)^{4}\), we will raise both the numerator and the denominator inside the parentheses to the power of 4. First, we raise the numerator: \[ (-3 x)^{4} = (-3)^{4} \cdot x^{4} = 81 x^{4}. \] Next, we raise the denominator: \[ (y^{3})^{4} = y^{3 \cdot 4} = y^{12}. \] Now we can combine these results: \[ \left(\frac{-3 x}{y^{3}}\right)^{4} = \frac{81 x^{4}}{y^{12}}. \] The final simplified expression is: \[ \frac{81 x^{4}}{y^{12}}. \]