Answer
$\dfrac{2\sqrt[4]{a^3}\sqrt[3]{c^2}}{\sqrt{b}}$
Work Step by Step
Using the laws of exponents, the given expression, $
2a^{3/4}b^{-1/2}c^{2/3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2a^{3/4}c^{2/3}}{b^{1/2}}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
\dfrac{2a^{3/4}c^{2/3}}{b^{1/2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2\sqrt[4]{a^3}\sqrt[3]{c^2}}{\sqrt{b}}
.\end{array}
