Let's solve the expression step by step:
The expression given is: \[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right) \]
- Multiply the first two terms:
\[ (-4) \times \left(\frac{7}{5}\right) = -\frac{28}{5} \]
- Multiply the result by the next term:
\[ \left(-\frac{28}{5}\right) \times \left(-\frac{3}{4}\right) = \frac{28 \times 3}{5 \times 4} = \frac{84}{20} \]
Now we can simplify \(\frac{84}{20}\):
\[ \frac{84}{20} = \frac{21}{5} \quad \text{(Dividing both the numerator and denominator by 4)} \]
- Now divide by \(\frac{7}{15}\):
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{21}{5} \div \left(\frac{7}{15}\right) = \frac{21}{5} \times \frac{15}{7} \]
- Multiply the fractions:
\[ = \frac{21 \times 15}{5 \times 7} = \frac{315}{35} \]
Now we simplify \(\frac{315}{35}\):
\[ \frac{315 \div 35}{35 \div 35} = 9 \]
Therefore, the final answer is:
\[ \boxed{9} \]