Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 433: 69

$24m^2$

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}