The expression is `5 * (18 - 3^2) + 24 / 6`. 1. First, evaluate the exponent inside the parentheses: `3^2 = 9`. The expression becomes `5 * (18 - 9) + 24 / 6`. 2. Next, complete the operation inside the parentheses: `18 - 9 = 9`. The expression becomes `5 * 9 + 24 / 6`. 3. Perform multiplication and division from left to right: `5 * 9 = 45`. `24 / 6 = 4`. The expression becomes `45 + 4`. 4. Finally, perform the addition: `45 + 4 = 49`. The simplified value of the expression is 49. Why others are wrong: A — Correct answer. B — This result occurs if `3^2` is incorrectly calculated as `3 * 2 = 6` instead of `3 * 3 = 9`. C — This result occurs if multiplication `5 * 18` is performed before simplifying the parentheses `(18 - 3^2)`, violating the order of operations. D — This result occurs if the student incorrectly groups operations by first evaluating `(18 - 3^2) + 24 / 6` and then multiplying the entire sum by `5`.

The expression to simplify is: 50 - (3 * 8 + 24 / 4) + 2^3 1. **Exponents first:** Calculate 2^3 = 8. The expression becomes: 50 - (3 * 8 + 24 / 4) + 8 2. **Parentheses next:** Inside the parentheses, perform multiplication and division from left to right. Calculate 3 * 8 = 24. Calculate 24 / 4 = 6. The expression inside parentheses becomes: 24 + 6 = 30. The overall expression is now: 50 - 30 + 8 3. **Addition and Subtraction last:** Perform these operations from left to right. Calculate 50 - 30 = 20. Calculate 20 + 8 = 28. The final simplified balance is 28. Why others are wrong: A — This result would be obtained if 2^3 was incorrectly calculated as 2*3=6. B — This is the correct answer. C — This result would be obtained if addition was performed before multiplication/division inside the parentheses (e.g., 3 * (8 + 24) / 4). D — This result would be obtained if the parentheses were largely ignored, and operations were performed mostly left-to-right after exponents, but still respecting multiplication/division over addition/subtraction.

1. Parentheses: First, evaluate the expression inside the parentheses: (7 - 2) = 5. The expression becomes 24 ÷ 3 × (5)² - 10. 2. Exponents: Next, evaluate the exponent: (5)² = 25. The expression becomes 24 ÷ 3 × 25 - 10. 3. Multiplication and Division (from left to right): Perform the division: 24 ÷ 3 = 8. The expression becomes 8 × 25 - 10. Perform the multiplication: 8 × 25 = 200. The expression becomes 200 - 10. 4. Addition and Subtraction (from left to right): Finally, perform the subtraction: 200 - 10 = 190. Why others are wrong: B — This result (350) occurs if the exponent `(7-2)²` is incorrectly calculated as `7² - 2² = 49 - 4 = 45`, leading to `24 ÷ 3 × 45 - 10 = 8 × 45 - 10 = 360 - 10 = 350`. C — This result (70) occurs if the exponent `(7-2)²` is incorrectly calculated as `(7-2) × 2 = 5 × 2 = 10`, leading to `24 ÷ 3 × 10 - 10 = 8 × 10 - 10 = 80 - 10 = 70`. D — This result (30) occurs if the exponent `( )²` is omitted entirely or treated as `(7-2) = 5` instead of `5²`, leading to `24 ÷ 3 × 5 - 10 = 8 × 5 - 10 = 40 - 10 = 30`.

Apply the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 1. **Parentheses/Brackets:** `(15 - 8) = 7` The expression becomes: `36 ÷ 3 + 4 × 7 - 2^3` 2. **Exponents/Orders:** `2^3 = 2 × 2 × 2 = 8` The expression becomes: `36 ÷ 3 + 4 × 7 - 8` 3. **Multiplication and Division (from left to right):** `36 ÷ 3 = 12` `4 × 7 = 28` The expression becomes: `12 + 28 - 8` 4. **Addition and Subtraction (from left to right):** `12 + 28 = 40` `40 - 8 = 32` The simplified value is 32. Why others are wrong: A — This result occurs if `2^3` is incorrectly calculated as `2 × 3 = 6`, leading to `12 + 28 - 6 = 34`. B — This result occurs if operations are performed strictly from left to right without adhering to BODMAS/PEMDAS (e.g., performing `12 + 4` before `4 × 7`), leading to `(12 + 4) × 7 - 8 = 16 × 7 - 8 = 112 - 8 = 104`. C — This result occurs if `(15 - 8)` is mistakenly calculated as `6` instead of `7`, leading to `36 ÷ 3 + 4 × 6 - 2^3 = 12 + 24 - 8 = 36 - 8 = 28`. D — This is the correct answer.

1. First, simplify the division within the parentheses: 18 ÷ 3 = 6. 2. Next, simplify the addition within the parentheses: 6 + 2 = 8. 3. Then, perform the multiplication: 8 × 4 = 32. 4. Finally, perform the subtraction: 32 - 10 = 22. Why others are wrong: A — This results from incorrectly ignoring the parentheses and performing operations from left to right (18 ÷ 3 + 2 × 4 - 10 = 6 + 8 - 10 = 4). C — This results from a calculation error where 8 × 4 is incorrectly evaluated as 36 instead of 32 (36 - 10 = 26). D — This results from a calculation error where 32 - 10 is incorrectly evaluated as 30.