# 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 $$0 assuming that $$lim_{n to infty}|a_n|$$ exists?