The diagram below shows the graph of
where e, sometimes known as Euler’s number is given by e=2.718281828459.
e=2.718281828459 is special because everywhere on this graph, the gradient is the same as the y-coordinate.
The graph of , however, for any a>1 is of a similar shape. If a=1, then you are calculating 1 to any power, which is always 1, and so this would be the graph of y=1. For a<1, the graph will be reflected in the y-axis. This is because when you multiply a number less than 1 by itself, it become smaller; that is, of course, unless the power is negative.