Answer
(a) $\frac{1}{x}$
(b) $\frac{xy^{4}}{8}$
Work Step by Step
(a) $(\frac{x^{-2/3}}{y^{1/2}})(\frac{x^{-2}}{y^{-3}})^{1/6}=x^{-2/3+-2*1/6}y^{-1/2-(-3)(1/6)}=\frac{1}{x}$
(b) $(\frac{x^{1/2}y^{2}}{2y^{1/4}})^{4}(\frac{4x^{-2}y^{-4}}{y^{2}})^{1/2}=x^{4*1/2}y^{2*4}2^{-1*4}y^{-1/4*4}4^{1/2}x^{-2*1/2}y^{-4*1/2}y^{-2*1/2}=x^2y^82^{-4}y^{-1}2x^{-1}y^{-2}y^{-1}=2^{-4+1}x^{2-1}y^{8-1-2-1}=\frac{xy^{4}}{8}$
