Math Problem Statement

Evaluate 3^(-2).

Solution

The image shows the expression 323^{-2}. This represents a number raised to a negative exponent.

To evaluate 323^{-2}, recall that a negative exponent means you take the reciprocal of the base raised to the positive exponent:

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

Thus, 32=193^{-2} = \frac{1}{9}.

Would you like a more detailed explanation or have any further questions about exponents?

Here are some related questions for you to explore:

  1. How do you simplify an expression with a negative exponent?
  2. What happens when you raise a number to the power of zero?
  3. How would you evaluate 232^{-3}?
  4. What is the rule for multiplying numbers with the same base but different exponents?
  5. How do fractional exponents relate to roots?

Tip: When dealing with negative exponents, always remember that they represent the reciprocal of the positive exponent!

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Exponents
Reciprocal Rules

Formulas

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

Theorems

Negative Exponent Rule

Suitable Grade Level

Grades 6-8