# Reference: OPPOWER

a^b = OPPOWER(a, b) returns a raised to the power of b. If a and b are complex numbers,
a^b = exp(b⋅ln(a)) (1)
as long as a ≠ 0. (If we are working with real numbers only, it is necessary that a > 0 in most cases.)
If b is a positive number, a^b = a⋅a⋅...⋅a, where the factor a occurs exactly b times. a^0 = 1 (the empty product) unless a = 0, for 0^0 is undefined. 0^b = 0 for all non-zero numbers b. a^-b = 1/a^b, and a^(1/n), for a integer n, is the nth root of a, i.e. one of the roots to the equation x^n = a. Furthermore, in general, (x^a)^b = x^(ab).
For real numbers, the following applies to a^(1/n): If a > 0 and n is even, there are two roots, and the positive root is returned (example: 16^(1/2) = 4). If a > 0 and n is odd, there is only one root.
For complex numbers, the primary definition (1) is used to compute most values. The principal branch of ln is utilized, where the argument of a complex number lies within ]-π, π].