Is it true that $lim_{n to infty}|a_n|^{r}=left(lim_{n to infty}|a_n|right)^{r}$ for $0<r<1$?


Is the (fractional) power rule true for the limit of a sequence $|a_n|$ at $n to infty$, that is

$$lim_{n to infty}|a_n|^{r}=left(lim_{n to infty}|a_n|right)^{r}$$ for $0<r<1$ assuming that $lim_{n to infty}|a_n|$ exists?