A^-n equals which of the following?

• A. the exponent is inverted
• B. the exponent becomes zero
• C. the base is inverted
• D. the reciprocal of a^n

Answer: (D)

Negative exponents turn into reciprocals. For any nonzero base a and positive n, a^-n equals 1 divided by a^n. This keeps the rule that multiplying a^n by a^-n gives a^0 = 1, so a^-n must be the reciprocal of a^n. For example, 3^-2 is 1/(3^2) = 1/9. Saying the exponent is inverted is vague and doesn’t specify taking the reciprocal of the whole value, while inverting the base would only match the result in the special case n = 1. And the exponent becoming zero isn’t correct, since it becomes negative, not zero. Remember, the base can’t be zero because division by zero is undefined.