To solve the expression, we can follow the order of operations (PEMDAS) and the rules for multiplying and dividing fractions.
First, we can simplify each fraction:
(-3/5) times (5/16) times (7/12) divided by (-3/16) times (-5/7)
= (-3/5) * (5/16) * (7/12) / (-3/16) * (-5/7)
Multiplying fractions:
= (-3 * 5 * 7) / (5 * 16 * 12) / (-3 * -5 * 16 * 7)
= (-3 * 5 * 7) / (5 * 16 * 12) / (3 * 5 * 16 * 7)
Multiplying the numerators together and the denominators together, we get:
= (-3 * 5 * 7) / (5 * 16 * 12 * 3 * 5 * 16 * 7)
Now, cancel any factors common to both the numerator and denominator:
= (-3 * 5 * 7) / (5 * 16 * 12 * 3 * 5 * 16 * 7)
= (-1) / (16 * 12 * 16)
= -1 / (3072)
So the solution to the expression (-3/5) times (5/16) times (7/12) divided by (-3/16) times (-5/7) is -1/3072.