Answer
$\sqrt[15]{64a^3b^5}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\sqrt[3]{b}\cdot\sqrt[5]{4a}
\\\\=
b^{\frac{1}{3}}\cdot (4a)^{\frac{1}{5}}
\\\\=
b^{\frac{5}{15}}\cdot (4a)^{\frac{3}{15}}
\\\\=
(b^5\cdot(4a)^3)^{\frac{1}{15}}
\\\\=
(b^5\cdot64a^3)^{\frac{1}{15}}
\\\\=
(64a^3b^5)^{\frac{1}{15}}
\\\\=
\sqrt[15]{64a^3b^5}
.\end{array}
