Definition:Power (Algebra)/Real Number

Definition
Let $x \in \R_{>0}$ be a (strictly) positive real number.

Let $r \in \R$ be a real number.

Complex Number
This definition can be extended to complex $r$:

Also see

 * Equivalence of Definitions of Number to Real Power


 * Exponentiation to Real Number is Extension of Exponentiation to Rational Number