The problem in the image involves using the correct order of operations (PEMDAS/BODMAS) to solve an expression. Let's break it down:

Given expression:

$5 + (3 \times 2)^2 \div 6$

Applying the order of operations (PEMDAS):

• Parentheses first: $(3 \times 2) = 6$ Now the expression becomes: $5 + 6^2 \div 6$

• Exponents next: $6^2 = 36$ So the expression simplifies to: $5 + 36 \div 6$

• Division comes next: $36 \div 6 = 6$ The expression now is: $5 + 6$

• Addition finally: $5 + 6 = 11$

Final answer:

The value of the expression is 11, but it seems the handwritten work shows 7 as the final result, which might be due to an error in applying the order of operations.

Do you need further clarification on this?

Here are some additional questions to explore:

1. What would happen if we changed the exponent to a different number?
2. Can you show how division by a decimal number would affect the result?
3. What if the parentheses contained a subtraction instead of multiplication?
4. How does the order of operations change if there are nested parentheses?
5. What other strategies can help avoid mistakes with order of operations?

Tip: Always handle exponents and parentheses first, as missing these steps can lead to incorrect results.