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