Answer
$24m^2$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\dfrac{8\sqrt[3]{54m^7}}{\sqrt[3]{2m}}
\\\\=
8\sqrt[3]{\dfrac{54m^7}{2m}}
\\\\=
8\sqrt[3]{27m^{7-1}}
\\\\=
8\sqrt[3]{27m^{6}}
\\\\=
8\cdot3m^2
\\\\=
24m^2
.\end{array}