Answer
(a) $\frac{x^{3}}{y^{1/5}}$
(b) $r^{4}$
Work Step by Step
(a) $(x^{-5}y^{1/3})^{-3/5}=x^{-5*-3/5}y^{(1/3)(-3/5)}=\frac{x^{3}}{y^{1/5}}$
(b) $(4r^{8}t^{-1/2})^{1/2}(32t^{-5/4})^{-1/5}=4^{1/2}r^{8*1/2}t^{(-1/2)(1/2)}(32)^{-1/5}f^{(-5/4)(-1/5)}=2r^{4}t^{-1/4}(\frac{1}{2})t^{1/4}=r^{4}t^{0}=r^{4}*1=r^{4}$
