The exponential function , [math]b^x[/math] , varies its behavior if the base, [math]b[/math], is negative or positive. If the base is negative, it is real for only some values of [math]x[/math]. If [math]x[/math] 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. [br]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.