Answer
$(4xy+5x^2)\sqrt[4]{xy^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To add/subtract the given expression, $ \sqrt[4]{256x^5y^6}+\sqrt[4]{625x^9y^2} ,$ 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]{256x^4y^4\cdot xy^2}+\sqrt[4]{625x^8\cdot xy^2} \\\\= \sqrt[4]{(4xy)^4\cdot xy^2}+\sqrt[4]{(5x^2)^4\cdot xy^2} \\\\= 4xy\sqrt[4]{xy^2}+5x^2\sqrt[4]{xy^2} .\end{array}
Note that all variables are assumed to have positive values.
Combining the like radicals results to
\begin{array}{l}\require{cancel}
(4xy+5x^2)\sqrt[4]{xy^2}
.\end{array}
