Well, since a negative exponent is equal to the inverse of the positive exponent, i.e. a^(-b) = 1/(a^b), you could perhaps explain it in terms of the inverse somehow. If you are writing a book for publication, as opposed to a school assignment or something, you probably shouldn't define an exponent as a positive whole number, because exponents can not only be negative, but can be fractional and/or complex as well. It would, to use an analogy we all understand here, be like saying Elements is a game with four different elements, earth, air, fire, and water, and then be stuck at explaining the presence of the 8 remaining elements, as well as 'other' cards. Also, I think that in your two stated definitions above, that those would be true whether or not b>c.