Answer
$-m^2p\sqrt[4]{mp^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
2\sqrt[4]{m^9p^6}-3m^2p\sqrt[4]{mp^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}
2\sqrt[4]{m^8p^4\cdot mp^2}-3m^2p\sqrt[4]{mp^2}
\\\\=
2\sqrt[4]{(m^2p)^4\cdot mp^2}-3m^2p\sqrt[4]{mp^2}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
2m^2p\sqrt[4]{mp^2}-3m^2p\sqrt[4]{mp^2}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(2m^2p-3m^2p)\sqrt[4]{mp^2}
\\\\=
-m^2p\sqrt[4]{mp^2}
.\end{array}
