Let's evaluate the given mathematical expression step by step:

The expression is:

$(-3)^2 + (-2)^3 \div 2 + 15$

Step-by-Step Evaluation:

1. Evaluate $(-3)^2$:
   $(-3)^2 = (-3) \times (-3) = 9$

2. Evaluate $(-2)^3$:
   $(-2)^3 = (-2) \times (-2) \times (-2) = -8$

3. Divide $(-2)^3$ by 2:
   $-8 \div 2 = -4$

4. Add all components together:
   $9 + (-4) + 15$

   First, $9 + (-4) = 5$
   Then, $5 + 15 = 20$

Final Answer:

$20$

Would you like more details, or do you have any questions?

Here are 5 related questions to expand on this:

1. How do powers of negative numbers differ when the exponent is even versus odd?
2. What is the general rule for dividing negative numbers?
3. Can you explain the order of operations (PEMDAS/BODMAS) in more detail?
4. How does negative sign affect the result of exponentiation?
5. How would this calculation change if there were parentheses around certain parts?

Tip: Always remember to follow the order of operations carefully—handle exponents first, then multiplication and division, and finally addition and subtraction.