## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$3-4\sqrt[3]{63}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the given expression is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{3}(\sqrt[3]{9}-4\sqrt[3]{21}) \\\\= \sqrt[3]{3}(\sqrt[3]{9})+\sqrt[3]{3}(-4\sqrt[3]{21}) .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{3}(\sqrt[3]{9})+\sqrt[3]{3}(-4\sqrt[3]{21}) \\\\= \sqrt[3]{3(9)}-4\sqrt[3]{3(21)} \\\\= \sqrt[3]{27}-4\sqrt[3]{63} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{27}-4\sqrt[3]{63} \\\\= \sqrt[3]{(3)^3}-4\sqrt[3]{63} \\\\= 3-4\sqrt[3]{63} .\end{array}