Answer
$2q^2\sqrt[3]{5q}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
6q^2\sqrt[3]{5q}-2q\sqrt[3]{40q^4}
,$ 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}
6q^2\sqrt[3]{5q}-2q\sqrt[3]{8q^3\cdot5q}
\\\\=
6q^2\sqrt[3]{5q}-2q\sqrt[3]{(2q)^3\cdot5q}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
6q^2\sqrt[3]{5q}-2q(2q)\sqrt[3]{5q}
\\\\=
6q^2\sqrt[3]{5q}-4q^2\sqrt[3]{5q}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(6q^2-4q^2)\sqrt[3]{5q}
\\\\=
2q^2\sqrt[3]{5q}
.\end{array}
