Multiply \( -\frac{6}{11} a^{3} b\left(-3 \frac{1}{5} a b^{2}\right) \)

To multiply the expression \( -\frac{6}{11} a^{3} b\left(-3 \frac{1}{5} a b^{2}\right) \), first convert the mixed number into an improper fraction: \(-3 \frac{1}{5} = -\frac{16}{5}\). Now, the expression becomes: \[ -\frac{6}{11} a^{3} b \left(-\frac{16}{5} a b^{2}\right). \] Next, multiply the fractions and the like terms: \[ -\frac{6}{11} \times -\frac{16}{5} = \frac{96}{55}, \] and for the variables: \[ a^{3} \times a = a^{4}, \quad b \times b^{2} = b^{3}. \] Combining everything, we have: \[ \frac{96}{55} a^{4} b^{3}. \] So the final answer is: \[ \frac{96}{55} a^4 b^3. \]