Let's solve the expression step by step:
\[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right) \]
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Multiplying the first two terms: Multiply \(-4\) and \(\frac{7}{5}\):
\[ (-4) \times \left(\frac{7}{5}\right) = -\frac{28}{5} \]
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Multiplying by the third term: Now, multiply \(-\frac{28}{5}\) and \(-\frac{3}{4}\):
\[ -\frac{28}{5} \times -\frac{3}{4} = \frac{28 \times 3}{5 \times 4} = \frac{84}{20} \]
We can simplify \(\frac{84}{20}\):
\[ \frac{84 \div 4}{20 \div 4} = \frac{21}{5} \]
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Dividing by the last term: Next, we need to divide \(\frac{21}{5}\) by \(\frac{7}{15}\):
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{21}{5} \div \frac{7}{15} = \frac{21}{5} \times \frac{15}{7} \]
Now multiply:
\[ = \frac{21 \times 15}{5 \times 7} = \frac{315}{35} = 9 \]
Thus, the final answer is:
\[ \boxed{9} \]