Answer
$\frac{2\sqrt[3] {12mn^2}}{55mn}$.
Work Step by Step
The given expression is
$=\frac{4\sqrt[3] {6m^2n}}{55\sqrt[3]{4m^4n^2}}$
Use division rule.
$=\frac{4}{55}\cdot \sqrt[3] {\frac{6m^2n}{4m^4n^2}}$
Reduce the fraction.
$=\frac{4}{55}\cdot \sqrt[3] {\frac{3}{2m^2n}}$
Multiply by the needed factors.
$=\frac{4}{55}\cdot \sqrt[3] {\frac{3}{2m^2n}}\cdot \sqrt[3] {\frac{2^2mn^2}{2^2mn^2}}$
Use multiplication rule.
$=\frac{4}{55}\cdot \sqrt[3] {\frac{3\cdot 2^2mn^2}{2m^2n\cdot 2^2mn^2}}$
Simplify.
$=\frac{4}{55}\cdot \sqrt[3] {\frac{12mn^2}{2^3m^3n^3}}$
Cube root the denominator.
$=\frac{4}{55}\cdot \frac{\sqrt[3] {12mn^2}}{2mn}$
Simplify.
$=\frac{2\sqrt[3] {12mn^2}}{55mn}$.