2010-II-39

Ans: C
$\begin{array}{rcl}
\dfrac{1}{\sqrt{a^3}} \div \dfrac{\sqrt{b}}{a} & = & \dfrac{1}{\sqrt{a^3}} \times \dfrac{a}{\sqrt{b}} \\
& = & a^\frac{-3}{2} \times ab^\frac{-1}{2} \\
& = & a^{\frac{-3}{2}+1} \times b^\frac{-1}{2} \\
& = & a^\frac{-1}{2}b^\frac{-1}{2} \\
& = & (ab)^\frac{-1}{2} \\
& = & \dfrac{1}{\sqrt{ab}} \\
& = & \dfrac{1}{\sqrt{ab}} \times \dfrac{\sqrt{ab}}{\sqrt{ab}} \\
& = & \dfrac{\sqrt{ab}}{ab}
\end{array}$