Identifying Power Functions

Which of the following functions are power functions?

$$\begin{array}{cc}f\left(x\right)=1& \text{Constant}\text{function}\\ f\left(x\right)=x& \text{Identity}\text{function}\\ f\left(x\right)=x^2& \text{Quadratic}\text{function}\\ f\left(x\right)=x^3& \text{Cubic}\text{function}\\ f\left(x\right)=\frac{1}{x}& \text{Reciprocal}\text{function}\\ f\left(x\right)=\frac{1}{x^2}& \text{Reciprocal}\text{squared}\text{function}\\ f\left(x\right)=\sqrt{x}& \text{Square}\text{root}\text{function}\\ f\left(x\right)=\sqrt[3]{x}& \text{Cube}\text{root}\text{function}\end{array}$$

OpenStax, Precalculus 2e · §3.3 Power Functions and Polynomial Functions · Example 1