Exponentiation
When it is a positive integer, the exponent indicates how many copies of the base are multiplied together. For example, . The base appears times in the repeated multiplication, because the exponent is . Here, is the "base", is the "exponent", and is the "power" or, more specifically, "3 raised to the 5th power".
The Singularity Is Near
Kurzweil explains that evolutionary progress is exponential because of positive feedback; the results of one stage are used to create the next stage. Exponential growth is deceptive, nearly flat at first until it hits what Kurzweil calls "the knee in the curve" then rises almost vertically. In fact Kurzweil believes evolutionary progress is super-exponential because more resources are deployed to the winning process. As an example of super-exponential growth Kurzweil cites the computer chip business. The overall budget for the whole industry increases over time, since the fruits of exponential growth make it an attractive investment; meanwhile the additional budget fuels more innovation which makes the industry grow even faster, effectively an example of "double" exponential growth.