The exponent will adjust for differences in the response error to the CBC questionnaire vs. the error in choices buyers make in the real world. It's generally found that there is more noise in buyer choices than respondent choices in the questionnaire, so the Exponent often takes on a value somewhere between .4 and 1.0 after tuning to real market shares.
(See more on this for details in the SSI Web documentation, under the Help. Search for "Exponent").
But, after adjusting for the Exponent you will likely find that simulated shares do not match actual market shares. We do NOT recommend you use the "External Effects" available within the SMRT simulator to adjust for these differences, as there are better methods. Please see the paper we wrote on this subject at http://sawtoothsoftware.com/download/techpap/externaleffects.pdf
The recommended methods described in this paper (especially the individual-level Utility Adjustment method for implementing external effects) are being implemented in the new market simulator that is currently in beta and being released in the next few weeks as part of Lighthouse (formerly known as SSI Web) v9.
But, you can also (with a bit of work) implement them manually within SMRT.