Answer
$(3x-2x^{2})\sqrt[4]{x^2y^3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$ To add/subtract the given expression, $ \sqrt[4]{81x^6y^3}-\sqrt[4]{16x^{10}y^3} ,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals. $\bf{\text{Solution Details:}}$ Extracting the factors of each radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[4]{81x^4\cdot x^2y^3}-\sqrt[4]{16x^{8}\cdot x^2y^3} \\\\= \sqrt[4]{(3x)^4\cdot x^2y^3}-\sqrt[4]{(2x^{2})^4\cdot x^2y^3} \\\\= 3x\sqrt[4]{x^2y^3}-2x^{2}\sqrt[4]{x^2y^3} .\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
(3x-2x^{2})\sqrt[4]{x^2y^3}
.\end{array}
