Answer
$2\sqrt[3]{x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
2\sqrt[3]{27x}-2\sqrt[3]{8x}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
2\sqrt[3]{27\cdot x}-2\sqrt[3]{8\cdot x}
\\\\=
2\sqrt[3]{(3)^2\cdot x}-2\sqrt[3]{(2)^3\cdot x}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
2(3)\sqrt[3]{x}-2(2)\sqrt[3]{x}
\\\\=
6\sqrt[3]{x}-4\sqrt[3]{x}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(6-4)\sqrt[3]{x}
\\\\=
2\sqrt[3]{x}
.\end{array}
