The way ElectricPavlov solved the problem is the short way. Here is the long way.
\(\frac{\sqrt[3]{162}}{\sqrt[3]{2}}\)
\(\frac{\sqrt[3]{27\times6}}{\sqrt[3]{2}}\)
\(\frac{\sqrt[3]{27}\sqrt[3]{6}}{\sqrt[3]{2}}\)
\(\frac{3\sqrt[3]{6}}{\sqrt[3]{2}}\)
\(\frac{3\sqrt[3]{6}\sqrt[3]{4}}{\sqrt[3]{2}\sqrt[3]{4}}\)
\(\frac{3\sqrt[3]{6\times4}}{\sqrt[3]{2\times4}}\)
\(\frac{3\sqrt[3]{24}}{\sqrt[3]{8}}\)
\(\frac{3\sqrt[3]{8\times3}}{\sqrt[3]{8}}\)
\(\frac{3\sqrt[3]{8}\sqrt[3]{3}}{\sqrt[3]{8}}\)
\(\frac{3\times2\sqrt[3]{3}}{\sqrt[3]{8}}\)
\(\frac{6\sqrt[3]{3}}{\sqrt[3]{8}}\)
\(\frac{6\sqrt[3]{3}}{2}\)
\(3\sqrt[3]{3}\)
.
