Introduction: A function of the form $y(x)=x^k$, with $k$ a non-negative integer is called a Positive integer power function.
Definition: A function of the form
\[
x^{-k}=\frac{1}{x^k},
\]
with $k$ a positive integer, is a negative integer power function.
Example: $f(x)=x^{-5}=\dfrac{1}{x^5}$ is an example of a negative integer power function.
Definition: A function of the form
\[
x^{-k}=\frac{1}{x^k},
\]
with $k$ a positive integer, is a negative integer power function.
Example: $f(x)=x^{-5}=\dfrac{1}{x^5}$ is an example of a negative integer power function.