A Generalization of Multiplicative Factors for Fractional Exponents

This thesis explores a generalization of expressing a number raised to a fractional

exponent, N1/n, as the product of n identical factors. We derive that for any posi-

tive real number N and positive integer n, the expression N1/n can be represented

1/n2
to formalize this relationship, providing a clear framework for understanding such

as the product of n copies of N multiplicative decompositions.

. A functional representation is introduced