Let's simplify the expression step-by-step. The expression given is:

$(8^2 + 36) \div 2 + 15$

Step 1: Follow the order of operations (PEMDAS):

1. Parentheses: Simplify inside the parentheses first.
2. Exponents: Handle any exponents within the parentheses.
3. Multiplication/Division: From left to right.
4. Addition/Subtraction: From left to right.

Step 2: Simplify the exponent inside the parentheses:

$8^2 = 64$ So the expression becomes: $(64 + 36) \div 2 + 15$

Step 3: Simplify inside the parentheses:

$64 + 36 = 100$ Now, the expression is: $100 \div 2 + 15$

Step 4: Division comes next:

$100 \div 2 = 50$ So now the expression is: $50 + 15$

Step 5: Finally, perform the addition:

$50 + 15 = 65$

So, the simplified value of the expression is 65.

Would you like more details or have any questions? Here are 5 related questions you might want to explore:

1. What is the difference between PEMDAS and BODMAS?
2. How would this expression change if the exponent was applied after the addition?
3. What if division and addition were swapped in this expression?
4. How do you deal with more complex expressions with nested parentheses?
5. Why is following the correct order of operations crucial in mathematics?

Tip: Always remember to handle exponents before moving to multiplication or division in expressions!