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".
Exponentiation
The exponential function is defined for all integer, fractional, real, and complex values of "x". In fact, the matrix exponential is well-defined for square matrices (in which case this exponential identity only holds when "x" and "y" commute), and is useful for solving systems of linear differential equations.