Answer
$a)$ $4a^{4}b$
$b)$ $8a^{9}b^{12}$
Work Step by Step
$a)$ $(8a^{6}b^{3/2})^{2/3}$
Raise each factor inside the parentheses to the power of $\dfrac{2}{3}$ and simplify:
$(8a^{6}b^{3/2})^{2/3}=(8^{2/3})a^{4}b=(\sqrt[3]{8^{2}})a^{4}b=4a^{4}b$
$b)$ $(4a^{6}b^{8})^{3/2}$
Raise each factor inside the parentheses to the power of $\dfrac{3}{2}$ and simplify:
$(4a^{6}b^{8})^{3/2}=(4^{3/2})a^{9}b^{12}=(\sqrt{4^{3}})a^{9}b^{12}=8a^{9}b^{12}$
