Negative Exponents math worksheet with Christmas-themed icons.

Let’s solve each problem one by one. We’ll use the rules of exponents, especially for negative and zero exponents.

Remember:
- Any number to the power of 0 is 1 (except 0⁰, which is undefined — but we don’t have that here).
- A negative exponent means “take the reciprocal” → a^(-n) = 1 / a^n
- When you square a negative number, it becomes positive: (-a)² = a²
- If there’s no exponent written, it’s just the number itself.

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Left column:

1. 1 =
→ This is just 1. No exponent? It stays 1.

2. 7^(-3) =
→ Negative exponent → 1 / 7³ = 1 / (7×7×7) = 1 / 343

3. (-4)^(-1) =
→ Negative exponent → 1 / (-4)¹ = -1/4

4. 8^(-3) =
→ 1 / 8³ = 1 / (8×8×8) = 1 / 512

5. (-7)² =
→ Square the number: (-7) × (-7) = 49

6. (-2) =
→ Just the number -2. No exponent.

7. (-3)⁰ =
→ Anything (non-zero) to the 0 power is 1 → so this is 1

8. (-9)² =
→ (-9) × (-9) = 81

9. (-4)² =
→ (-4) × (-4) = 16

10. 9^(-2) =
→ 1 / 9² = 1 / 81

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Right column:

1. 2² =
→ 2 × 2 = 4

2. 10² =
→ 10 × 10 = 100

3. (-10)^(-1) =
→ 1 / (-10) = -1/10

4. (-1)² =
→ (-1) × (-1) = 1

5. 5^(-2) =
→ 1 / 5² = 1 / 25

6. 9² =
→ 9 × 9 = 81

7. 3^(-2) =
→ 1 / 3² = 1 / 9

8. 5² =
→ 5 × 5 = 25

9. (-7)^(-1) =
→ 1 / (-7) = -1/7

10. 3^(-2) =
→ Same as above → 1 / 9

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Now let’s write all answers in order.

Final Answer:
1 = 1
7^(-3) = 1/343
(-4)^(-1) = -1/4
8^(-3) = 1/512
(-7)² = 49
(-2) = -2
(-3)⁰ = 1
(-9)² = 81
(-4)² = 16
9^(-2) = 1/81

2² = 4
10² = 100
(-10)^(-1) = -1/10
(-1)² = 1
5^(-2) = 1/25
9² = 81
3^(-2) = 1/9
5² = 25
(-7)^(-1) = -1/7
3^(-2) = 1/9