Exponent Rules Notes and Worksheets - Lindsay Bowden - Free Printable

Here's the complete solution to the worksheet on Negative Exponents, with explanations for each problem.

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📌 Key Rules to Remember:

1. Negative Exponent Rule:
For any nonzero number `a` and positive integer `n`:
> a^(-n) = 1 / a^n

2. Zero Exponent Rule:
For any nonzero number `a`:
> a⁰ = 1

3. Positive Exponent Rule:
Just compute as usual:
> aⁿ = a × a × ... × a (n times)

4. Even vs Odd Powers of Negative Numbers:
- Even power → result is positive
- Odd power → result is negative

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## ✔ Solutions:

Left Column:

1. 5^(-2) = 1 / 5² = 1/25

2. 2^(-3) = 1 / 2³ = 1/8

3. (-9)^(-1) = 1 / (-9)¹ = -1/9

4. (-3)⁰ = 1 *(any nonzero number to the 0 power is 1)*

5. 7^(-1) = 1 / 7¹ = 1/7

6. (-9)^(-2) = 1 / (-9)² = 1 / 81 = 1/81
*(Note: (-9)² = 81, since even power makes it positive)*

7. (-9)^(-1) = same as #3 → -1/9

8. 10^(-1) = 1 / 10 = 1/10

9. (-1)² = (-1) × (-1) = 1

10. 10^(-2) = 1 / 10² = 1/100

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Right Column:

1. 5 = 5 *(no exponent shown → exponent is 1)*

2. (-7)² = (-7) × (-7) = 49

3. 1^(-3) = 1 / 1³ = 1 / 1 = 1

4. (-1)² = (-1) × (-1) = 1

5. 9^(-2) = 1 / 9² = 1/81

6. 6^(-3) = 1 / 6³ = 1 / 216 = 1/216

7. (-5)^(-2) = 1 / (-5)² = 1 / 25 = 1/25

8. (-10)^(-2) = 1 / (-10)² = 1 / 100 = 1/100

9. (-2)⁰ = 1 *(any nonzero base to the 0 power is 1)*

10. (-5)² = (-5) × (-5) = 25

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## 🧾 Final Answer Sheet:

```
Left Column:
5^(-2) = 1/25
2^(-3) = 1/8
(-9)^(-1) = -1/9
(-3)^0 = 1
7^(-1) = 1/7
(-9)^(-2) = 1/81
(-9)^(-1) = -1/9
10^(-1) = 1/10
(-1)^2 = 1
10^(-2) = 1/100

Right Column:
5 = 5
(-7)^2 = 49
1^(-3) = 1
(-1)^2 = 1
9^(-2) = 1/81
6^(-3) = 1/216
(-5)^(-2) = 1/25
(-10)^(-2) = 1/100
(-2)^0 = 1
(-5)^2 = 25
```

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✔ Tip for Students: Always remember — negative exponents mean “flip to denominator” (if numerator) or “flip to numerator” (if denominator). Zero exponent always equals 1 (as long as base ≠ 0).

Let me know if you’d like a printable version or step-by-step video explanation! 😊