Math Problem Statement

Simplify this expression: 3^(-2). Use 3 as the base.

Solution

The given expression is 323^{-2}.

To simplify it using only positive exponents, apply the rule of negative exponents:

an=1ana^{-n} = \frac{1}{a^n}

So:

32=132=193^{-2} = \frac{1}{3^2} = \frac{1}{9}

Thus, the simplified form is 19\frac{1}{9}.

Let me know if you want additional clarifications!

Expanding knowledge:

  1. What is the general rule for simplifying ana^{-n}?
  2. How do negative exponents affect fractional bases?
  3. How can negative exponents appear in equations involving variables?
  4. What happens when you multiply two terms with negative exponents?
  5. How does 323^{-2} compare to (3)2(-3)^{-2}?

Tip: Always simplify negative exponents by rewriting them as fractions to make computations easier!

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Math Problem Analysis

Mathematical Concepts

Negative Exponents
Exponential Notation
Simplification Rules

Formulas

a^(-n) = 1 / a^n

Theorems

Negative Exponent Rule

Suitable Grade Level

Grades 6-8