To solve the expression \((8/9) \times (-3/4) \div (1/9) \times (-4/5) \div (3/5)\), we will follow the order of operations and the properties of multiplication and division.
- Substitute the division with multiplication by the reciprocal:
- \(\div (1/9)\) becomes \(\times (9/1)\)
- \(\div (3/5)\) becomes \(\times (5/3)\)
This gives us: \[ (8/9) \times (-3/4) \times (9/1) \times (-4/5) \times (5/3) \]
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Now we can rearrange the expression: \[ = (8 \times -3 \times 9 \times -4 \times 5) / (9 \times 4 \times 5 \times 3) \]
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Simplify step by step:
- The numerators: \(8 \times -3 = -24\)
- \(-24 \times 9 = -216\)
- \(-216 \times -4 = 864\)
- \(864 \times 5 = 4320\)
The numerator after simplification: \[ 4320 \]
The denominator:
- \(9 \times 4 = 36\)
- \(36 \times 5 = 180\)
- \(180 \times 3 = 540\)
The denominator after simplification: \[ 540 \]
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Now we have: \[ \frac{4320}{540} \]
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Simplify the fraction: \(\frac{4320 \div 60}{540 \div 60} = \frac{72}{9} = 8\)
Thus, the final answer is: \[ \boxed{8} \]