AMC 12 2020a Problem 13

There are integers $a$, $b$, and $c$, each greater than 1, such that$$\sqrt[a]{N \sqrt[b]{N \sqrt[c]{N}}} = \sqrt[36]{N^{25}}$$for all $N > 1$. What is $b$?

\textbf{(A)}\ 2 \textbf{(B)}\ 3 \textbf{(C)}\ 4 \textbf{(D)}\ 5 \textbf{(E)}\ 6