#### Answer

$-7\sqrt[3]{ x^2y}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
3\sqrt[3]{x^2y}-5\sqrt[3]{8x^2y}
,$ 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}
3\sqrt[3]{x^2y}-5\sqrt[3]{8\cdot x^2y}
\\\\=
3\sqrt[3]{x^2y}-5\sqrt[3]{(2)^3\cdot x^2y}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
3\sqrt[3]{x^2y}-5(2)\sqrt[3]{ x^2y}
\\\\=
3\sqrt[3]{x^2y}-10\sqrt[3]{ x^2y}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3-10)\sqrt[3]{ x^2y}
\\\\=
-7\sqrt[3]{ x^2y}
.\end{array}