Let's solve the expression step by step:
We have:
\[ \left(-4\right) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right) \]
First, we'll handle the multiplication part:
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Multiply \(-4\) by \(\frac{7}{5}\): \[ -4 \times \frac{7}{5} = \frac{-4 \times 7}{5} = \frac{-28}{5} \]
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Next, multiply \(\frac{-28}{5}\) by \(-\frac{3}{4}\): \[ \frac{-28}{5} \times -\frac{3}{4} = \frac{-28 \times -3}{5 \times 4} = \frac{84}{20} \]
To simplify \(\frac{84}{20}\), we divide both the numerator and the denominator by their greatest common divisor (which is 4): \[ \frac{84 \div 4}{20 \div 4} = \frac{21}{5} \]
Now, we have simplified the multiplication part to:
\[ \frac{21}{5} \]
Next, we need to divide \(\frac{21}{5}\) by \(\frac{7}{15}\): To divide by a fraction, we multiply by its reciprocal: \[ \frac{21}{5} \div \frac{7}{15} = \frac{21}{5} \times \frac{15}{7} \]
Now we multiply: \[ = \frac{21 \times 15}{5 \times 7} \]
Calculating the numerator and denominator:
- Numerator: \(21 \times 15 = 315\)
- Denominator: \(5 \times 7 = 35\)
So, we have: \[ \frac{315}{35} \]
To simplify this fraction, we can divide both the numerator and the denominator by 35: \[ \frac{315 \div 35}{35 \div 35} = \frac{9}{1} = 9 \]
Thus, the final answer to the expression is \(\boxed{9}\).