Answer
$ f(x)=x^{-4/3}$ is contiuous on $(-\infty,0)\cup(0,\infty)$.
Work Step by Step
Since $ x^{-4/3}$ is defined for all $ x\neq 0$ then the domain of $ f(x)=x^{-4/3}$ is $(-\infty,0)\cup(0,\infty)$. Now, since $ x^{-4/3}$ is continous for all $ x\neq 0$, then by using the continuity laws, $ f(x)=x^{-4/3}$ is contiuous on $(-\infty,0)\cup(0,\infty)$.
