Certain responses from students of different school levels, regarding the non-natural exponents, have appealed our attention for two reasons: Such responses do not allow the building of skills and are related with a form of knowledge which we have called mathematic conventions. To this extent we know these have not been an explicit object of study at other researches. The above situation has led us to perform a study with the purpose of elaborating explanations, in terms of the interactions of the didactic system, based on those responses from the students. The results of this study allow us to establish the necessary elements in order to understand the depth of the related didactic phenomena and also gives us the basis for the discussion of the didactic operation of the mathematic conventions. Furthermore, we seek to shape a line of investigation that will intend to determine in which sense the mathematic conventions can be considered as pieces of the social building of knowledge.