To simplify the expression \((−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)\), let's first rewrite the division as multiplication by the reciprocal.
The division can be rewritten as follows:
\[ (−3/5)×(5/16)×(7/12)×\left(\frac{-16}{3}\right)×\left(-\frac{7}{5}\right) \]
Now, using the Associative Property of Multiplication and Commutative Property of Multiplication, we can rearrange and group the terms. We can rewrite the expression as:
\[ (−3)×(−16)×(−5) \div (5)×(7)×(16)×(12) \quad \text{all divided by } 3. \]
Next, we'll multiply the fractions:
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Combine the numerators: \[ (-3) \times (5) \times (7) \times (-16) \times (-5) = (-3) \times (-5) \times (-5) \times (7) \times 16 \]
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Combine the denominators: \[ (5) \times (16) \times (12) \times (3). \]
Now, let's write all this together: \[ \frac{(-3)(-16)(-5)(7)}{(5)(16)(12)(-3)(-5)} \]
Now, we can simplify. We see that the -3 in the numerator and denominator cancel out.
So we can rewrite as: \[ \frac{(-5)(7)(-16)}{(5)(16)(12)(-5)}. \]
Now group the terms again: \[ \frac{(-5)(7)(-16)}{(-5)(5)(16)(12)} = \frac{7}{5*12} = \frac{7/5}{12} = \frac{7}{60}. \]
Thus, the result of the expression is: \[ \boxed{\frac{7}{60}}. \]