We can simplify the expression step by step:

$9 \div 3 \cdot (5^2 - 18) + 2$

Step 1: Simplify the exponent

$5^2 = 25$ So the expression becomes: $9 \div 3 \cdot (25 - 18) + 2$

Step 2: Simplify inside the parentheses

$25 - 18 = 7$ Now the expression is: $9 \div 3 \cdot 7 + 2$

Step 3: Perform division

$9 \div 3 = 3$ Now it becomes: $3 \cdot 7 + 2$

Step 4: Multiply

$3 \cdot 7 = 21$ Now it is: $21 + 2$

Step 5: Add the final terms

$21 + 2 = 23$

Thus, the value of the expression is $23$.

Would you like more details on any of the steps? Here are some related questions to explore further:

1. How does the order of operations (PEMDAS) affect solving expressions like this?
2. Can you explain how to solve expressions involving both multiplication and division?
3. What happens if the parentheses are removed in such expressions?
4. How do you simplify expressions with larger exponents?
5. What are some common mistakes when solving such multi-step problems?

Tip: Always simplify expressions inside parentheses first to avoid mistakes with the order of operations.