I'll solve each problem step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to right).
Problem 1: 8 + (4² - 12) + 4³
- First, calculate exponents inside parentheses: 4² = 16
- Then subtract in parentheses: 16 - 12 = 4
- Calculate the other exponent: 4³ = 64
- Now add: 8 + 4 + 64 = 76
Problem 2: 4 × (-6) ÷ 8 + 3³
- First, calculate the exponent: 3³ = 27
- Multiply and divide from left to right: 4 × (-6) = -24, then -24 ÷ 8 = -3
- Add: -3 + 27 = 24
Problem 3: (6³ - 6) × (2³ + 8) ÷ 2
- Calculate exponents in first parentheses: 6³ = 216, so 216 - 6 = 210
- Calculate exponents in second parentheses: 2³ = 8, so 8 + 8 = 16
- Multiply: 210 × 16 = 3360
- Divide: 3360 ÷ 2 = 1680
Problem 4: 8³ + (7 - 1)² + 5
- Calculate the subtraction in parentheses: 7 - 1 = 6
- Calculate exponents: 8³ = 512 and 6² = 36
- Add: 512 + 36 + 5 = 553
Problem 5: 81 ÷ 9 + (9 + 5)² + 3³
- Calculate addition in parentheses: 9 + 5 = 14
- Calculate exponents: 14² = 196 and 3³ = 27
- Divide: 81 ÷ 9 = 9
- Add: 9 + 196 + 27 = 232
Problem 6: 8² × (3 + 2) - 11
- Calculate addition in parentheses: 3 + 2 = 5
- Calculate exponent: 8² = 64
- Multiply: 64 × 5 = 320
- Subtract: 320 - 11 = 309
Problem 7: (2 × 4 + 1)³ - 6 ÷ 2
- Calculate multiplication in parentheses: 2 × 4 = 8
- Add in parentheses: 8 + 1 = 9
- Calculate exponent: 9³ = 729
- Divide: 6 ÷ 2 = 3
- Subtract: 729 - 3 = 726
Problem 8: (24 - 15)² + 2⁴ ÷ 2
- Calculate subtraction in parentheses: 24 - 15 = 9
- Calculate exponents: 9² = 81 and 2⁴ = 16
- Divide: 16 ÷ 2 = 8
- Add: 81 + 8 = 89
Problem 9: 2 + 5² - (4 × 6)
- Calculate exponent: 5² = 25
- Calculate multiplication in parentheses: 4 × 6 = 24
- Add and subtract from left to right: 2 + 25 = 27, then 27 - 24 = 3
Problem 10: 7³ ÷ (-7) + 7³ + 4
- Calculate exponents: 7³ = 343 (appears twice)
- Divide: 343 ÷ (-7) = -49
- Add from left to right: -49 + 343 = 294, then 294 + 4 = 298
Final Answer:
1. 76
2. 24
3. 1680
4. 553
5. 232
6. 309
7. 726
8. 89
9. 3
10. 298
Parent Tip: Review the logic above to help your child master the concept of order of operations with exponents worksheet.
