Answer
Choice D
Work Step by Step
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression, $
\sqrt[3]{\dfrac{a^2}{b^6}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{a^2}{b^6}}
\\\\=
\dfrac{\sqrt[3]{a^2}}{\sqrt[3]{b^6}}
\\\\=
\dfrac{\sqrt[3]{a^2}}{\sqrt[3]{(b^2)^3}}
\\\\=
\dfrac{\sqrt[3]{a^2}}{b^2}
.\end{array}
Hence, $\text{
Choice D
.}$
