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

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UpStudy AI · Accepted Answer

To multiply the expressions $$ -\frac{6}{11} a^{3} b $$ and $$ -3 \frac{1}{5} a b^{2} $$, follow these steps:

1. **Convert Mixed Number to Improper Fraction:**
   $$
   -3 \frac{1}{5} = -\frac{16}{5}
   $$

2. **Rewrite the Expression:**
   $$
   \left(-\frac{6}{11} a^{3} b\right) \times \left(-\frac{16}{5} a b^{2}\right)
   $$

3. **Multiply the Coefficients:**
   $$
   \left(-\frac{6}{11}\right) \times \left(-\frac{16}{5}\right) = \frac{96}{55}
   $$

4. **Multiply the Like Variables:**
   - For $$ a $$:
     $$
     a^{3} \times a = a^{4}
     $$
   - For $$ b $$:
     $$
     b \times b^{2} = b^{3}
     $$

5. **Combine Everything:**
   $$
   \frac{96}{55} a^{4} b^{3}
   $$

**Final Answer:**
$$
\frac{96}{55}\, a^{4}\, b^{3}
$$
The product is $$ \frac{96}{55} a^{4} b^{3} $$.

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