The construction of the exponential function of a real exponent from the definition of the powers of a real number, and its properties, requires the notion of successions, a decimal approximation of a rational number, convergence, and limit of a function. In Argentina, this construction would exceed what could be taught at the secondary level, but it provides advanced students of teachers in mathematics, and teachers in practice, the possibility of discussing what happens in the case of irrational exponents of the type ap, or discuss the validity of the properties of this type of power.