What definitions do you have to work with? Certainly, for and positive integers, you can think of " " as meaning "a multiplied by itself times" so that is "(a multiplied by itself times) multiplied by itself times" so that is a multiplied by itself a total of times. Then, the standard procedure is to define define for b negative, a fraction, and an irrational number so that , , and so that is a continuous function of b.