To solve the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\), we will follow the order of operations and handle the multiplication and division involving signed numbers.
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Multiply the first two numbers: \[ (-4) \times \left(\frac{7}{5}\right) = -\frac{28}{5} \]
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Now multiply the result by \(-\frac{3}{4}\): \[ -\frac{28}{5} \times \left(-\frac{3}{4}\right) = \frac{28 \times 3}{5 \times 4} = \frac{84}{20} = \frac{21}{5} \quad \text{(since both negatives cancel out)} \]
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Now divide the result by \(\frac{7}{15}\): \[ \frac{21}{5} \div \left(\frac{7}{15}\right) = \frac{21}{5} \times \left(\frac{15}{7}\right) \]
Now multiply: \[ \frac{21 \times 15}{5 \times 7} = \frac{315}{35} = 9 \]
Thus, the final result of the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\) is: \[ \boxed{9} \]