Is $2^{O(\sqrt{\log (\log^3 n)})} = 2^{O(\sqrt{\log \log n})}$?

Question

As the question states, I am reading somewhere that:

$$2^{O(\sqrt{\log (\log^3 n)})} = 2^{O(\sqrt{\log \log n})}$$

I don't quite see why, though, as $\log^3 n \neq O(\log n)$?