9. For all real numbers $x$, let
$$
f(x)=\frac{1}{\sqrt[2011]{1-x^{2011}}} .
$$

Evaluate $(f(f(\ldots(f(2011)) \ldots)))^{2011}$, where $f$ is applied 2010 times.
Answer: $2011^{2011}$ Direct calculation shows that $f(f(x))=\frac{\sqrt[2011]{1-x^{2011}}}{-x}$ and $f(f(f(x)))=x$. Hence $(f(f(\ldots(f(x)) \ldots)))=x$, where $f$ is applied 2010 times. So $(f(f(\ldots(f(2011)) \ldots)))^{2011}=$ $2011^{2011}$.