The negative exponent rule states that for any non-zero number \(a\) and any integer \(n\), the expression \(a^{-n}\) is equal to \(\frac{1}{a^n}\). This means that when you have a negative exponent, you take the reciprocal of the base and make the exponent positive. 

Here's the rule in mathematical terms:

\[a^{-n} = \frac{1}{a^n}\]

### Example:

1. \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\)
2. \(5^{-2} = \frac{1}{5^2} = \frac{1}{25}\)
3. \(10^{-1} = \frac{1}{10^1} = \frac{1}{10}\)

### Application:

If you encounter a negative exponent in an expression, you can rewrite the expression without the negative exponent by taking the reciprocal. This is useful for simplifying and solving equations.

### Detailed Steps:

1. **Identify the base and the negative exponent:** Look for the term with a negative exponent.
2. **Apply the negative exponent rule:** Convert the term with the negative exponent to its reciprocal with a positive exponent.
3. **Simplify if necessary:** Perform any additional arithmetic or algebraic simplifications.

Would you like more details or have any specific questions?

Here are some questions you might be interested in:

1. How do you simplify expressions with negative exponents and multiple variables?
2. How do you solve equations that include negative exponents?
3. What is the relationship between negative exponents and division?
4. How do negative exponents apply to fractional bases?
5. How can you convert a negative exponent to a positive one in a complex expression?

**Tip:** When working with negative exponents, always remember to flip the base to its reciprocal to make the exponent positive. This will help in simplifying and solving expressions accurately.

Explore the negative exponent rule in mathematics: a^{-n} = \frac{1}{a^n}. Learn how to simplify expressions with negative exponents with detailed examples and step-by-step explanations. Suitable for Grades 7-9 students and anyone interested in algebraic rules.

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