The expression \( 9^{-2} \) can be simplified by following the rules for negative exponents. Specifically, \( a^{-n} = \frac{1}{a^n} \).

So:
\[
9^{-2} = \frac{1}{9^2} = \frac{1}{81}
\]

Therefore, \( 9^{-2} = \frac{1}{81} \).

Would you like more details or have any questions?

1. How do negative exponents work in general?
2. What happens if the base is a fraction or decimal with a negative exponent?
3. How can we simplify \( 3^{-4} \) using similar steps?
4. What is the difference between \( 9^2 \) and \( 9^{-2} \) in terms of value?
5. How do negative exponents relate to roots and fractional exponents?

**Tip:** Negative exponents essentially "flip" the base number into its reciprocal form, making calculations easier when they appear in equations.

Explore the concept of negative exponents with the example 9^-2. Learn how to simplify it using exponent rules and reciprocal properties. This guide covers key exponent principles for middle school students, ideal 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