What does an exponent denote when it is used in the form of a fraction?

When an exponent is expressed in the form of a fraction, it signifies how many times the base is multiplied by itself. This applies when dealing with positive integer exponents; for example, in the expression ( a^n ), the base ( a ) is multiplied by itself ( n ) times. In the case of fractional exponents, they can represent both roots and powers, such as ( a^{1/n} ) indicating the nth root of ( a ), and ( a^{m/n} ) signifying both taking the nth root and raising to the mth power.

The choice reflecting how many times the base is multiplied aligns with the foundational understanding of exponentiation, reinforcing its definition in the context of mathematical operations.