A3. Let $b=\sqrt[2019]{\sqrt[2018]{\ldots \sqrt[4]{\sqrt[3]{\sqrt[2]{a}}}}}, a>0$. Which expression is equivalent to $\sqrt[2020]{\sqrt[2019]{\sqrt[2018]{\ldots \sqrt[4]{\sqrt[3]{a^{404}}}}}}$?
(A) $\sqrt[2020]{b}$
(B) $\sqrt[5]{b}$
(C) $\sqrt[5]{b^{2}}$
(D) $b^{404}$
(E) $b^{202}$
A3. The second expression is very similar to expression $b$, except that instead of $\sqrt[2]{a}$ we have $a^{404}$. We can write $a^{404}$ as $\sqrt[2]{a^{808}}$. Altogether, we can transform it into $\sqrt[2020]{b^{808}}=\sqrt[5]{b^{2}}$.