Let's solve each of the exponent expressions step by step from the worksheet:
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1. $ 5^2 + 3^3 $
- $ 5^2 = 5 \times 5 = 25 $
- $ 3^3 = 3 \times 3 \times 3 = 27 $
- $ 25 + 27 = 52 $
✔ Answer: 52
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2. $ 2^6 + 4^2 $
- $ 2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64 $
- $ 4^2 = 4 \times 4 = 16 $
- $ 64 + 16 = 80 $
✔ Answer: 80
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3. $ 7^2 - 20^1 $
- $ 7^2 = 7 \times 7 = 49 $
- $ 20^1 = 20 $
- $ 49 - 20 = 29 $
✔ Answer: 29
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4. $ 3^2 \times 2^2 $
- $ 3^2 = 9 $
- $ 2^2 = 4 $
- $ 9 \times 4 = 36 $
✔ Answer: 36
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5. $ 9^2 + 18 $
- $ 9^2 = 81 $
- $ 81 + 18 = 99 $
✔ Answer: 99
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6. $ 0^7 - 1^{15} $
- $ 0^7 = 0 $ (any positive power of 0 is 0)
- $ 1^{15} = 1 $ (any power of 1 is 1)
- $ 0 - 1 = -1 $
✔ Answer: -1
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7. $ 99^1 + 10^2 $
- $ 99^1 = 99 $
- $ 10^2 = 100 $
- $ 99 + 100 = 199 $
✔ Answer: 199
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8. $ 10^4 + 0^{12} $
- $ 10^4 = 10,000 $
- $ 0^{12} = 0 $ (since 0 to any positive power is 0)
- $ 10,000 + 0 = 10,000 $
✔ Answer: 10,000
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9. $ 2^8 - 11^2 $
- $ 2^8 = 256 $
- $ 11^2 = 121 $
- $ 256 - 121 = 135 $
✔ Answer: 135
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10. $ 6^4 + 3^4 $
- $ 6^4 = 6 \times 6 \times 6 \times 6 = 1296 $
- $ 3^4 = 3 \times 3 \times 3 \times 3 = 81 $
- $ 1296 + 81 = 1377 $
✔ Answer: 1377
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11. $ 5^2 \times 1^{201} $
- $ 5^2 = 25 $
- $ 1^{201} = 1 $
- $ 25 \times 1 = 25 $
✔ Answer: 25
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12. $ 1^{12} - 9^1 $
- $ 1^{12} = 1 $
- $ 9^1 = 9 $
- $ 1 - 9 = -8 $
✔ Answer: -8
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | 52 |
| 2 | 80 |
| 3 | 29 |
| 4 | 36 |
| 5 | 99 |
| 6 | -1 |
| 7 | 199 |
| 8 | 10,000 |
| 9 | 135 |
| 10 | 1377 |
| 11 | 25 |
| 12 | -8 |
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🔍 Key Concepts Used:
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Exponentiation: $ a^n $ means multiplying $ a $ by itself $ n $ times.
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Order of Operations: Exponents come before addition/subtraction and multiplication/division.
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Special Cases:
- $ 0^n = 0 $ for $ n > 0 $
- $ 1^n = 1 $ for any $ n $
- $ a^1 = a $
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of adding exponents worksheet.
