Question

1. evaluate: 2 × (4^2 - 2)
2. evaluate: 12 ÷ (3^2 - 1) + 2
3. evaluate: (3^2 + 2) × (5 - 2)
4. evaluate: (8 + 2^3) - 10

challenge problem
evaluate: (2^3 + 5) × (4 - 2) + 12 ÷ 4

Explanation:

Problem 2

Step1: Calculate exponent inside parentheses

$4^2 = 16$

Step2: Subtract inside parentheses

$16 - 2 = 14$

Step3: Multiply by the outer term

$2 \times 14 = 28$

Problem 3

Step1: Calculate exponent inside parentheses

$3^2 = 9$

Step2: Subtract inside parentheses

$9 - 1 = 8$

Step3: Divide 12 by the result

$12 \div 8 = 1.5$

Step4: Add the final term

$1.5 + 2 = 3.5$

Problem 4

Step1: Calculate exponent inside first parentheses

$3^2 = 9$

Step2: Add inside first parentheses

$9 + 2 = 11$

Step3: Subtract inside second parentheses

$5 - 2 = 3$

Step4: Multiply the two results

$11 \times 3 = 33$

Problem 5

Step1: Calculate exponent inside parentheses

$2^3 = 8$

Step2: Add inside parentheses

$8 + 8 = 16$

Step3: Subtract the final term

$16 - 10 = 6$

Challenge Problem

Step1: Calculate exponent inside first parentheses

$2^3 = 8$

Step2: Add inside first parentheses

$8 + 5 = 13$

Step3: Subtract inside second parentheses

$4 - 2 = 2$

Step4: Multiply the two parentheses results

$13 \times 2 = 26$

Step5: Calculate the division term

$12 \div 4 = 3$

Step6: Add the two results

$26 + 3 = 29$

Answer:

Problem 2: 28
Problem 3: 3.5
Problem 4: 33
Problem 5: 6
Challenge Problem: 29