#### Answer

Choice A

#### Work Step by Step

Using the properties of radicals, the expression, $
\dfrac{\sqrt[3]{a^6}}{\sqrt[3]{b^9}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{a^6}}{\sqrt[3]{b^9}}
\\\\=
\dfrac{\sqrt[3]{(a^2)^3}}{\sqrt[3]{(b^3)^3}}
\\\\=
\dfrac{a^2}{b^3}
.\end{array}
Note that the variable/s is/are assumed to be positive.
Hence, $\text{
Choice A
.}$