Exponentiation

Exponentiation is a mathematical operation ab = a multiplied by itself b times. For example, 33 = 3 &times; 3 &times; 3 = 27. It is ubiquitous in modern mathematics.

Formally,  = , where   is the exponential function and ln is the natural logarithm, which are defined like so:


 * \(e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots\)
 * \(\ln x = \int_1^x \frac{dt}{t}\)

This allows the definition to be expanded to non-integer values of b.

ab is typically pronounced "a to the bth power" or just "a to the bth."