Math worksheet for practicing negative exponents with 20 problems.

It looks like the image contains a worksheet titled "Negative Exponents", and it asks you to evaluate expressions with negative exponents. However, there's a small confusion: all the exponents listed are positive, not negative.

Let’s clarify:

The expressions shown are:
```
2⁻³ = | 3⁻² =
6⁻² = | 2⁻² =
5⁻² = | 9⁻² =
10⁻³ = | 1⁻³ =
3⁻³ = | 5⁻³ =
4⁻² = | 2⁻⁴ =
7⁻² = | 4⁻³ =
8⁻² = | 10⁻⁴ =
10⁻² = | 11⁻² =
```

But in your image, they're written as positive exponents (like `2^3`, `6^2`, etc.). That might be a typo or mislabeling.

However, since the title says "Negative Exponents", and the expressions have negative exponents (as shown above), we will assume that the correct problem is to evaluate these expressions with negative exponents, even if the image shows positive ones.

---

🔷 Rule for Negative Exponents:

$$
a^{-n} = \frac{1}{a^n}
$$

We’ll use this rule to evaluate each expression.

---

✔ Left Column:

1. $ 2^{-3} = \frac{1}{2^3} = \frac{1}{8} $

2. $ 6^{-2} = \frac{1}{6^2} = \frac{1}{36} $

3. $ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} $

4. $ 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} $

5. $ 3^{-3} = \frac{1}{3^3} = \frac{1}{27} $

6. $ 4^{-2} = \frac{1}{4^2} = \frac{1}{16} $

7. $ 7^{-2} = \frac{1}{7^2} = \frac{1}{49} $

8. $ 8^{-2} = \frac{1}{8^2} = \frac{1}{64} $

9. $ 10^{-2} = \frac{1}{10^2} = \frac{1}{100} $

---

✔ Right Column:

1. $ 3^{-2} = \frac{1}{3^2} = \frac{1}{9} $

2. $ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} $

3. $ 9^{-2} = \frac{1}{9^2} = \frac{1}{81} $

4. $ 1^{-3} = \frac{1}{1^3} = \frac{1}{1} = 1 $

5. $ 5^{-3} = \frac{1}{5^3} = \frac{1}{125} $

6. $ 2^{-4} = \frac{1}{2^4} = \frac{1}{16} $

7. $ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} $

8. $ 10^{-4} = \frac{1}{10^4} = \frac{1}{10000} $

9. $ 11^{-2} = \frac{1}{11^2} = \frac{1}{121} $

---

📝 Final Answers:

| Expression | Value |
|----------|-------|
| $2^{-3}$ | $ \frac{1}{8} $ |
| $6^{-2}$ | $ \frac{1}{36} $ |
| $5^{-2}$ | $ \frac{1}{25} $ |
| $10^{-3}$ | $ \frac{1}{1000} $ |
| $3^{-3}$ | $ \frac{1}{27} $ |
| $4^{-2}$ | $ \frac{1}{16} $ |
| $7^{-2}$ | $ \frac{1}{49} $ |
| $8^{-2}$ | $ \frac{1}{64} $ |
| $10^{-2}$ | $ \frac{1}{100} $ |

| Expression | Value |
|----------|-------|
| $3^{-2}$ | $ \frac{1}{9} $ |
| $2^{-2}$ | $ \frac{1}{4} $ |
| $9^{-2}$ | $ \frac{1}{81} $ |
| $1^{-3}$ | $ 1 $ |
| $5^{-3}$ | $ \frac{1}{125} $ |
| $2^{-4}$ | $ \frac{1}{16} $ |
| $4^{-3}$ | $ \frac{1}{64} $ |
| $10^{-4}$ | $ \frac{1}{10000} $ |
| $11^{-2}$ | $ \frac{1}{121} $ |

---

🔍 Explanation:

- A negative exponent means you take the reciprocal of the base raised to the positive exponent.
- For example: $ a^{-n} = \frac{1}{a^n} $
- This rule applies to any non-zero base.

> ⚠️ Note: $ 0^{-n} $ is undefined (division by zero), but none of these involve zero.

Let me know if you'd like this explained further or formatted differently!