Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 25

$2+\sqrt[3]{20}$

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ \sqrt[3]{2}(\sqrt[3]{4}+\sqrt[3]{10}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{2}(\sqrt[3]{4})+\sqrt[3]{2}(\sqrt[3]{10}) \\\\= \sqrt[3]{8}+\sqrt[3]{20} \\\\= \sqrt[3]{(2)^3}+\sqrt[3]{20} \\\\= 2+\sqrt[3]{20} .\end{array}