Answer
$a)$ $2ab\sqrt[6]{b}$
$b)$ $4a^{2}\sqrt[3]{b^{2}}$
Work Step by Step
$a)$ $\sqrt[6] {64a^{6}b^{7}}$
$\sqrt[6] {64a^{6}b^{7}}=(\sqrt[6] {64})(\sqrt[6]{a^{6}})(\sqrt[6]{b^{7}})=(2)(a)(b\sqrt[6]{b})=2ab\sqrt[6]{b}$
$b)$ $\sqrt[3]{a^{2}b}\sqrt[3]{64a^{4}b}$
$\sqrt[3]{a^{2}b}\sqrt[3]{64a^{4}b}=\sqrt[3]{(a^{2}b)(64a^{4}b)}=\sqrt[3]{64a^{6}b^{2}}=(\sqrt[3]{64})(\sqrt[3]{a^{6}})(\sqrt[3]{b^{2}})$
$...=(4)(a^{2})(\sqrt[3]{b^{2}})=4a^{2}\sqrt[3]{b^{2}}$
