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 tilting
In Monte Carlo Estimation, exponential tilting (ET), exponential twisting, or exponential change of measure (ECM) is a distribution shifting technique commonly used in rare-event simulation, and rejection and importance sampling in particular. Exponential tilting is also used in Esscher tilting, an indirect Edgeworth approximation technique. The earliest formalization of ECM is often attributed to Esscher with its use in importance sampling being attributed to David Siegmund. ET is known as the Esscher transform in mathematical finance and is used in such contexts as insurance futures pricing.