Exponential Function
Description
The exponential function ,  , varies its behavior if the base, , is negative or positive.  If the base is negative, it is real for only some values of .  If  is a rational number with an odd denominator, the denominator portion gives a real negative number results.  If the numerator is even the final result is positive and if the numerator is odd, the final result is negative.  
In this applet , if the base is negative, rational numbers with 5, 7, and 9 in the denominator are shown.  If the base is positive the smooth curve is shown.