Which of the following is equivalent to the expression 3^(-2)?

Question

Accepted Answer

1/9. A negative exponent indicates the reciprocal of the base raised to the positive exponent: a^(-n) = 1/(a^n). Therefore, 3^(-2) = 1/(3^2) = 1/9. The negative exponent does NOT make the result negative  -  it moves the base from the numerator to the denominator (or vice versa).

"-9" (-9) is a very common misconception. Students often interpret the negative sign in the exponent as making the base negative, computing -(3^2) = -9. But a negative exponent means "take the reciprocal," not "negate the result." "-6" (-6) might come from multiplying 3 × (-2) = -6, incorrectly treating exponentiation as multiplication. "1/6" (1/6) might come from computing 1/(3 × 2) instead of 1/(3^2).

Negative exponents are a crucial concept on the CLEP exam. Key rules include: a^(-n) = 1/a^n, (a/b)^(-n) = (b/a)^n, and a^(-1) = 1/a. Combined with other exponent rules, negative exponents allow simplification of complex expressions. For example, (2^(-3))(2^5) = 2^(-3+5) = 2^2 = 4. Also, (x^(-2))/(x^(-5)) = x^(-2-(-5)) = x^3. Being comfortable with negative exponents is essential for working with scientific notation, rational expressions, and exponential functions.

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