What does a negative exponent indicate?

A negative exponent indicates that the base of the exponent should be taken as a reciprocal. For instance, if you have a number raised to a negative exponent, such as ( a^{-n} ), this means that the expression can be rewritten as ( \frac{1}{a^n} ). This transformation reflects the inverse relationship indicated by the negative sign; thus, a negative exponent effectively flips the base to its reciprocal. The concept is foundational in algebra, as it aligns with the properties of exponents which dictate how numbers interact under multiplication and division.

The other choices involve misinterpretations of what a negative exponent signifies. While it's true that negative exponents involve division (as expressed through the reciprocal), the core concept here is that it explicitly indicates a reciprocal transformation, which is fundamental to understanding the purpose of negative exponents in mathematical expressions. Understanding this principle is crucial for manipulating algebraic expressions correctly and applying exponent rules effectively.