What index indicates reciprocal and is represented as a^(-n) = 1/a^n?

The concept of an index, or exponent, reflects how many times a number (the base) is multiplied by itself. When an index is negative, it indicates the reciprocal of the base raised to the corresponding positive index.

In the case of a negative index, the expression ( a^{-n} ) means that instead of multiplying ( a ) by itself ( n ) times, you are taking the number 1 divided by ( a ) raised to the power of ( n ). Thus, ( a^{-n} = \frac{1}{a^n} ). This relationship highlights that a negative index effectively inverts the base and then applies the positive exponent.

By contrast, positive indices, whole number indices, and fractional indices serve different functions. A positive index increases the power of the base, a whole number index also consists of non-negative integers, and a fractional index denotes roots or powers that yield a fraction. None of these options describe the inversion that occurs with a negative index. Hence, the definition aligns perfectly with the concept of a negative index.