Write in ascending order the numbers: $\sqrt{121}$, $\sqrt[3]{729}$, and $\sqrt[4]{38416}$.
Factoring the numbers and extracting the roots we have:

$$
\begin{aligned}
& \sqrt{121}=\sqrt{11^{2}}=11 \\
& \sqrt[3]{729}=\sqrt[3]{9^{3}}=9 \\
& \sqrt[4]{38416}=\sqrt[4]{2^{4} \times 7^{4}}=2 \times 7=14
\end{aligned}
$$

Therefore, in ascending order we have: $\sqrt[3]{729}, \sqrt{121}, \sqrt[4]{38416}$.