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 (multiplication and division from left to right).
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Multiplying the first two numbers: \[ (-4) \times \left(\frac{7}{5}\right) = \frac{-4 \times 7}{5} = \frac{-28}{5} \]
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Continuing with the next multiplication: \[ \frac{-28}{5} \times \left(-\frac{3}{4}\right) = \frac{-28 \times -3}{5 \times 4} = \frac{84}{20} \]
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Simplifying \(\frac{84}{20}\): \[ \frac{84}{20} = \frac{21}{5} \quad \text{(dividing the numerator and denominator by 4)} \]
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Now, we will divide by \(\frac{7}{15}\): Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{21}{5} \div \left(\frac{7}{15}\right) = \frac{21}{5} \times \left(\frac{15}{7}\right) = \frac{21 \times 15}{5 \times 7} \]
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Calculating the multiplication: \[ = \frac{315}{35} \]
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Simplifying \(\frac{315}{35}\): \[ = 9 \quad \text{(divide both the numerator and denominator by 35)} \]
Now let's compile all the steps: The final result is \(9\).
Thus, the answer is: 9