Answer
$-5\sqrt[3]{ x^2y^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
3\sqrt[3]{x^2y^2}-2\sqrt[3]{64x^2y^2}
,$ 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^2}-2\sqrt[3]{64\cdot x^2y^2}
\\\\=
3\sqrt[3]{x^2y^2}-2\sqrt[3]{(4)^3\cdot x^2y^2}
.\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^2}-2(4)\sqrt[3]{ x^2y^2}
\\\\=
3\sqrt[3]{x^2y^2}-8\sqrt[3]{ x^2y^2}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3-8)\sqrt[3]{ x^2y^2}
\\\\=
-5\sqrt[3]{ x^2y^2}
.\end{array}
