The problem is to evaluate the expression $(-3)^2 \div (-2) \times (-4)^2$.

1. Problem Description

The problem is to evaluate the expression $(-3)^2 \div (-2) \times (-4)^2$.

2. Solution Steps

We need to follow the order of operations (PEMDAS/BODMAS). First, we evaluate the exponents:

$(-3)^2 = (-3) \times (-3) = 9$

$(-4)^2 = (-4) \times (-4) = 16$

Now we have $9 \div (-2) \times 16$.

Next, we perform division and multiplication from left to right.

$9 \div (-2) = -\frac{9}{2} = -4.5$

Finally, we multiply:

$-4.5 \times 16 = -72$

3. Final Answer

-72