## Intermediate Algebra (12th Edition)

$-m^2p\sqrt[4]{mp^2}$
$\bf{\text{Solution Outline:}}$ 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^2\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}