Quotient rule of radicals – cannot get to correct answer

I am to simplify the following expression:

$ \sqrt(9a^5b^{14}) / \sqrt(3a^4b^5)$

The solution is given:

$ b4\sqrt3ab$

I was unable to recreate this solution. Here’s where I got to. Using the quotient rule I rewrote the expression as:

$ \sqrt(9a^5b^{14}) / (3a^4b^5)$

Then, I attempted to simplify (the radicand?):

$ (9a^5b^{14}) / (3a^4b^5)$

Becomes:

$ \sqrt3ab^9$

My train of thought is that first, I simplify $ 9a^5 / 3a^4$ to just $ 3a$ . Is that right?

Next I tried to simplify $ b^{14} / b^5$ to $ b^9$

Thus I arrived at $ \sqrt3ab^9$

Where did I go wrong and am I on the right track?