To simplify the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\), we can follow these steps:
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Handle the multiplication first: \[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \]
- Multiply \(-4\) and \(-\frac{3}{4}\): \[ -4 \times -\frac{3}{4} = 3 \]
- Now, multiply this by \(\frac{7}{5}\): \[ 3 \times \frac{7}{5} = \frac{21}{5} \]
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Now, handle the division by \(\frac{7}{15}\): \[ \frac{21}{5} \div \frac{7}{15} \] When dividing by a fraction, you can multiply by its reciprocal: \[ \frac{21}{5} \times \frac{15}{7} \]
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Multiply the fractions: \[ \frac{21 \times 15}{5 \times 7} \]
- Calculate \(21 \times 15 = 315\)
- Calculate \(5 \times 7 = 35\)
- So, we have: \[ \frac{315}{35} \]
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Simplify \(\frac{315}{35}\): \[ 315 \div 35 = 9 \]
Thus, the final result is: \[ \boxed{9} \]