Divide the following and reduce the answer to its simplest terms. \[ \frac{-10}{3} \div \frac{6}{7} \]

To divide fractions, you multiply by the reciprocal of the second fraction. So, we take the given expression: \[ \frac{-10}{3} \div \frac{6}{7} = \frac{-10}{3} \times \frac{7}{6} \] Now, multiply the numerators and denominators together: \[ = \frac{-10 \times 7}{3 \times 6} = \frac{-70}{18} \] Next, we need to reduce \(\frac{-70}{18}\) to its simplest terms. The greatest common divisor (GCD) of 70 and 18 is 2. Dividing both the numerator and denominator by 2 gives: \[ \frac{-70 \div 2}{18 \div 2} = \frac{-35}{9} \] Thus, the answer, in its simplest terms, is: \[ \frac{-35}{9} \]