Power functions with natural numbers as exponent

A power function with a natural as exponent is a function of the form $f(x)=a\cdot x^{n}f(x)=a\backslash cdot\; x^n$ ($n\in \mathbb{N},a\in \mathbb{R}n\backslash in\; \backslash mathbb\{N\},\; a\backslash in\; \backslash mathbb\{R\}$)

The form of the power function depends on the exponent $nn$ and on the coefficient $aa$.

Example

The volume of a sphere with radius r is given by the expression $V(r)=\frac{4}{3}\pi \cdot r^{3}V(r)=\backslash frac\{4\}\{3\}\backslash pi\backslash cdot\; r^3$. Here, $V(r)V(r)\%$ is a power function with exponent 3 and coefficient $\frac{4}{3}\pi \backslash frac\{4\}\{3\}\backslash pi$.