6. [5] We say " $s$ grows to $r$ " if there exists some integer $n>0$ such that $s^{n}=r$. Call a real number $r$ "sparse" if there are only finitely many real numbers $s$ that grow to $r$. Find all real numbers that are sparse.
Answer: $\quad-1,0,1$ For any number $x$, other than these $3, x, \sqrt[3]{x}, \sqrt[5]{x}, \sqrt[7]{x}, \ldots$ provide infinitely many possible values of $s$, so these are the only possible sparse numbers. On the other hand, -1 is the only possible value of $s$ for $r=-1,0$ is the only value for $r=0$, and -1 and 1 are the only values for $r=1$. Therefore, $-1,0$, and 1 are all sparse.