Extra explanation: alternative notation | Wiskunde op Tilburg University

Definition: A function of the form

$y(x)=x^{\frac{m}{n}}$ , with

$m$ and

$n$ integers (

$n \neq 0$ ), is called a power function.

Extra explanation: If

$n$ and

$m$ are positive, then we define for all

$x\geq 0$ the power function as follows:

$x^{\frac{m}{n}}=\sqrt[n]{x^m},$
and hence, for all

$x>0$ ,

$x^{-\frac{m}{n}}=\dfrac{1}{\sqrt[n]{x^m}}.$