#### Answer

$(4+3xy)\sqrt[3]{xy^2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt[3]{64xy^2}+\sqrt[3]{27x^4y^5}
,$ 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}
\sqrt[3]{64\cdot xy^2}+\sqrt[3]{27x^3y^3\cdot xy^2}
\\\\=
\sqrt[3]{(4)^3\cdot xy^2}+\sqrt[3]{(3xy)^3\cdot xy^2}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
4\sqrt[3]{xy^2}+3xy\sqrt[3]{xy^2}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(4+3xy)\sqrt[3]{xy^2}
.\end{array}