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 $x>0$,
\[
x^{-\frac{m}{n}}=\dfrac{1}{\sqrt[n]{x^m}}.
\]
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 $x>0$,
\[
x^{-\frac{m}{n}}=\dfrac{1}{\sqrt[n]{x^m}}.
\]