Answer
$3\sqrt[3]{4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To add/subtract the given expression, $
\sqrt[3]{32}-5\sqrt[3]{4}+2\sqrt[3]{108}
,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals.
$\bf{\text{Solution Details:}}$
Extracting the factors of each radicand that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{8\cdot4}-5\sqrt[3]{4}+2\sqrt[3]{27\cdot4}
\\\\=
\sqrt[3]{(2)^3\cdot4}-5\sqrt[3]{4}+2\sqrt[3]{(3)^3\cdot4}
\\\\=
2\sqrt[3]{4}-5\sqrt[3]{4}+2(3)\sqrt[3]{4}
\\\\=
2\sqrt[3]{4}-5\sqrt[3]{4}+6\sqrt[3]{4}
.\end{array}
By combining the like radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
(2-5+6)\sqrt[3]{4}
\\\\=
3\sqrt[3]{4}
.\end{array}
