To solve the expression \((9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right)\), we will simplify it step by step using properties of multiplication and division.
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Rewrite the division as multiplication by the reciprocal:
\[ 9 \div \left(\frac{5}{4}\right) = 9 \times \left(\frac{4}{5}\right) \]
\[ \Rightarrow 9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right) = 9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right) \]
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Combine the fractions and numbers:
\[ = 9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right) \]
Notice that the \(9\) in the numerator and \(9\) in the denominator can cancel:
\[ = \frac{9 \cdot 4 \cdot 7 \cdot (-5) \cdot 2}{5 \cdot 9 \cdot 7} \]
After canceling out the \(9\) and the \(7\):
\[ = \frac{4 \cdot (-5) \cdot 2}{5} \]
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Calculate the remaining values:
\[ = \frac{4 \cdot (-10)}{5} = \frac{-40}{5} = -8 \]
Thus, the final result is
\[ \boxed{-8} \]
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