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".
Exponential function
For the real exponential function is a constant and the derivative is zero because formula_3 for positive and the real exponential functions are monotonically increasing (as depicted for and ), because the derivative is greater than zero for all arguments, and for they are monotonically decreasing (as depicted for ), because the derivative is less than zero for all arguments.