Power exponential function is like both power function and exponential function, both of which have their own characteristics. As a power function, its power exponent is determined as a constant, and the power base is an independent variable; On the contrary, the exponential function has a fixed radix, and the exponent is an independent variable. Power exponential function is a function in which power base and power exponent are independent variables. The generalization of this function is the generalized power exponential function.

A function with the shape is called a power exponential function. In other words, it is like a power function and an exponential function, and they have both characteristics. As a power function, its power exponent is determined as a constant, and the power base is an independent variable; On the contrary, the exponential function has a fixed radix, and the exponent is an independent variable. Power exponential function is a function in which power base and power exponent are independent variables. The generalization of this function is the generalized power exponential function.