Negative exponents indicate that the base should be reciprocated (or taken as the inverse). Here's a detailed explanation:

1. **Basic Concept:**
   For any non-zero number \(a\) and a positive integer \(n\),
   \[
   a^{-n} = \frac{1}{a^n}
   \]

2. **Examples:**
   - \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)
   - \( 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \)
   - \( 10^{-1} = \frac{1}{10} = 0.1 \)

3. **Properties:**
   - \(\left(\frac{1}{a}\right)^n = a^{-n}\)
   - \((a^m)^n = a^{m \cdot n}\), even if \(n\) is negative.

4. **Combining with Positive Exponents:**
   - \(a^m \cdot a^{-n} = a^{m-n}\)
   - \(\frac{a^m}{a^n} = a^{m-n}\)

5. **Working with Fractions:**
   If you have a fraction with a negative exponent, you can take the reciprocal of the fraction and make the exponent positive:
   \[
   \left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n
   \]

Would you like details or have any questions?

Here are 5 example questions you could ask:
1. How do I simplify expressions with both positive and negative exponents?
2. Can you explain the rules for multiplying and dividing exponents?
3. What is the significance of an exponent of zero?
4. How do negative exponents apply to scientific notation?
5. Can you solve an equation involving negative exponents?

**Tip:** When working with exponents, remember to apply the exponent rules consistently to avoid mistakes.

Explore negative exponents with detailed explanations and examples. Learn how to interpret and apply negative exponents in mathematical expressions. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation