  In his monograph, H. Gonshor showed that Conway's real closed field of
surreal numbers carries an exponential and logarithmic map. Subsequently, L.
van den Dries and P. Ehrlich showed that it is a model of the elementary theory
of the field of real numbers with the exponential function. In this paper, we
give a complete description of the exponential equivalence classes in the
spirit of the classical Archimedean and multiplicative equivalence classes.
This description is made in terms of a recursive formula as well as a sign
sequence formula for the family of representatives of minimal length of these
exponential classes.
