Exponents Worksheet with 20 math problems involving powers and bases, including positive, negative, and zero exponents.

Sure! Let’s solve each problem on the Exponents Worksheet step by step and explain the rules used.

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🔢 Key Exponent Rules Used:

1. Any number to the power of 0 is 1 — *except 0⁰, which is undefined*.
2. Zero to any positive power is 0: `0ⁿ = 0` for `n > 0`.
3. One to any power is 1: `1ⁿ = 1`.
4. Negative base with even exponent → positive result.
5. Negative base with odd exponent → negative result.
6. aⁿ = a × a × ... × a (n times).

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## ✔ Solutions:

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1 a. 0¹⁷

→ Any positive power of 0 is 0.
✔ Answer: 0

1 b. 10⁴

→ 10 × 10 × 10 × 10 = 10,000
✔ Answer: 10,000

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2 a. 5²

→ 5 × 5 = 25
✔ Answer: 25

2 b. (–10)⁷

→ Negative base, odd exponent → result is negative.
→ 10⁷ = 10,000,000 → so (–10)⁷ = –10,000,000
✔ Answer: –10,000,000

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3 a. 7²

→ 7 × 7 = 49
✔ Answer: 49

3 b. (–4)¹

→ Any number to the power of 1 is itself → –4
✔ Answer: –4

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4 a. (–100)⁶

→ Negative base, even exponent → result is positive.
→ 100⁶ = (10²)⁶ = 10¹² = 1,000,000,000,000
✔ Answer: 1,000,000,000,000

4 b. (–4)³

→ Negative base, odd exponent → result is negative.
→ 4³ = 64 → so (–4)³ = –64
✔ Answer: –64

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5 a. 1⁴⁷

→ 1 raised to any power is always 1.
✔ Answer: 1

5 b. (–2)⁶

→ Negative base, even exponent → result is positive.
→ 2⁶ = 64 → so (–2)⁶ = 64
✔ Answer: 64

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6 a. 5³

→ 5 × 5 × 5 = 125
✔ Answer: 125

6 b. (–8)¹

→ Any number to the power of 1 is itself → –8
✔ Answer: –8

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7 a. (–3)³

→ Negative base, odd exponent → result is negative.
→ 3³ = 27 → so (–3)³ = –27
✔ Answer: –27

7 b. 7¹

→ Any number to the power of 1 is itself → 7
✔ Answer: 7

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8 a. 0⁴

→ Zero to any positive power is 0.
✔ Answer: 0

8 b. (–3)¹

→ Same as above → –3
✔ Answer: –3

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9 a. 100³

→ 100 × 100 × 100 = 1,000,000
✔ Answer: 1,000,000

9 b. 0²³

→ Zero to any positive power is 0.
✔ Answer: 0

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10 a. (–9)¹

→ Any number to the power of 1 is itself → –9
✔ Answer: –9

10 b. 0³⁶

→ Zero to any positive power is 0.
✔ Answer: 0

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## 📋 Final Answer Key:

| Problem | Answer |
|---------|------------------|
| 1a | 0 |
| 1b | 10,000 |
| 2a | 25 |
| 2b | –10,000,000 |
| 3a | 49 |
| 3b | –4 |
| 4a | 1,000,000,000,000|
| 4b | –64 |
| 5a | 1 |
| 5b | 64 |
| 6a | 125 |
| 6b | –8 |
| 7a | –27 |
| 7b | 7 |
| 8a | 0 |
| 8b | –3 |
| 9a | 1,000,000 |
| 9b | 0 |
| 10a | –9 |
| 10b | 0 |

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Let me know if you’d like this in printable format or need help understanding any specific rule! 😊