CAT 2025 Slot 1 — QA Question 19

For any natural number $k$, let $a_k=3^k$. The smallest natural number $m$ for which $\left\{\left(a_1\right)^1 \times\left(a_2\right)^2 \times \ldots \times\left(a_{20}\right)^{20}\right\}<\left\{a_{21} \times a_{22} \times \ldots \times a_{(20+m)}\right\}$, is