Grade 9 Zero and Negative Exponents Worksheets 2024 - Free Printable

Let's solve each problem from the worksheet on Zero and Negative Exponents. The goal is to simplify each expression so that only positive exponents appear in the final answer.

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Rules to Remember:

1. Any non-zero number raised to the power of 0 is 1:
$ a^0 = 1 $ (for $ a \neq 0 $)

2. Negative exponents:
$ a^{-n} = \frac{1}{a^n} $

3. When moving terms with negative exponents, move them to the denominator (or numerator) to make the exponent positive.

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Now, let’s go through each problem one by one:

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#### 1. $ 2^0 $

Using rule 1:
$ 2^0 = 1 $

✔ Answer: $ \boxed{1} $

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#### 2. $ 2^{-1} $

Using rule 2:
$ 2^{-1} = \frac{1}{2^1} = \frac{1}{2} $

✔ Answer: $ \boxed{\frac{1}{2}} $

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#### 3. $ (-2)^{-1} $

$ (-2)^{-1} = \frac{1}{(-2)^1} = \frac{1}{-2} = -\frac{1}{2} $

✔ Answer: $ \boxed{-\frac{1}{2}} $

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#### 4. $ (-5)^{-1} $

$ (-5)^{-1} = \frac{1}{(-5)} = -\frac{1}{5} $

✔ Answer: $ \boxed{-\frac{1}{5}} $

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#### 5. $ (8a)^{-2} $

First, apply the exponent to both parts:
$ (8a)^{-2} = \frac{1}{(8a)^2} = \frac{1}{8^2 \cdot a^2} = \frac{1}{64a^2} $

✔ Answer: $ \boxed{\frac{1}{64a^2}} $

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#### 6. $ 2u^{-1}v^{-2} $

Move negative exponents to the denominator:
$ 2u^{-1}v^{-2} = \frac{2}{u^1 v^2} = \frac{2}{uv^2} $

✔ Answer: $ \boxed{\frac{2}{uv^2}} $

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#### 7. $ 2p^{-1}q^{-1} $

Move both variables to the denominator:
$ 2p^{-1}q^{-1} = \frac{2}{p q} $

✔ Answer: $ \boxed{\frac{2}{pq}} $

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#### 8. $ 3a^{-2}b^{-1} $

Move $ a^{-2} $ and $ b^{-1} $ to denominator:
$ 3a^{-2}b^{-1} = \frac{3}{a^2 b} $

✔ Answer: $ \boxed{\frac{3}{a^2b}} $

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#### 9. $ a^{-4}b^{-3} $

Move both to denominator:
$ a^{-4}b^{-3} = \frac{1}{a^4 b^3} $

✔ Answer: $ \boxed{\frac{1}{a^4b^3}} $

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#### 10. $ a^{-2}b^3 $

Only $ a^{-2} $ has a negative exponent:
$ a^{-2}b^3 = \frac{b^3}{a^2} $

✔ Answer: $ \boxed{\frac{b^3}{a^2}} $

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#### 11. $ 2u^{-1}v^{-1} $

Move both negative exponents:
$ 2u^{-1}v^{-1} = \frac{2}{u v} $

✔ Answer: $ \boxed{\frac{2}{uv}} $

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#### 12. $ 2x^{-1}b^2 $

Only $ x^{-1} $ has a negative exponent:
$ 2x^{-1}b^2 = \frac{2b^2}{x} $

✔ Answer: $ \boxed{\frac{2b^2}{x}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1. $ 2^0 $ | $ 1 $ |
| 2. $ 2^{-1} $ | $ \frac{1}{2} $ |
| 3. $ (-2)^{-1} $ | $ -\frac{1}{2} $ |
| 4. $ (-5)^{-1} $ | $ -\frac{1}{5} $ |
| 5. $ (8a)^{-2} $ | $ \frac{1}{64a^2} $ |
| 6. $ 2u^{-1}v^{-2} $ | $ \frac{2}{uv^2} $ |
| 7. $ 2p^{-1}q^{-1} $ | $ \frac{2}{pq} $ |
| 8. $ 3a^{-2}b^{-1} $ | $ \frac{3}{a^2b} $ |
| 9. $ a^{-4}b^{-3} $ | $ \frac{1}{a^4b^3} $ |
| 10. $ a^{-2}b^3 $ | $ \frac{b^3}{a^2} $ |
| 11. $ 2u^{-1}v^{-1} $ | $ \frac{2}{uv} $ |
| 12. $ 2x^{-1}b^2 $ | $ \frac{2b^2}{x} $ |

Let me know if you'd like this formatted as a printable answer sheet!