#### Answer

$2a^{}b^{3}\sqrt[4]{5a}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[4]{20a^3b^7}\sqrt[4]{4a^2b^5}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{20a^3b^7(4a^2b^5)}
\\\\=
\sqrt[4]{80a^{3+2}b^{7+5}}
\\\\=
\sqrt[4]{80a^{5}b^{12}}
\\\\=
\sqrt[4]{16a^{4}b^{12}\cdot5a}
\\\\=
\sqrt[4]{(2a^{}b^{3})^4\cdot5a}
\\\\=
2a^{}b^{3}\sqrt[4]{5a}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.