Final answer:
The definition described is for negative exponents, indicating that a negative exponent on a real number other than 0 means taking the reciprocal of the base raised to the positive of that exponent.
Step-by-step explanation:
The definition in question relates to the concept of negative exponents in mathematics. It states that if a is a real number other than 0 and n is an integer, then a-n = 1/an. This means that a negative exponent indicates that the base, in this case a, is to be taken as the reciprocal raised to the positive of that exponent.
For example, using this rule, if we have 3-4, this would be the same as 1/34, which further simplifies to 1/(3×3×3×3). This expresses the idea that as you 'move' a number to the denominator, you must flip the sign of the exponent, turning a negative exponent into a positive one, which aligns with the general concept that operations have inverse operations, e.g., subtraction is the inverse of addition. Understanding the rule for negative exponents can be useful in a wide variety of mathematical contexts, from simplifying algebraic expressions to solving equations.