Answer
$a)$ $\dfrac{x^{3}}{\sqrt[5]{y}}$
$b)$ $r^{4}$
Work Step by Step
$a)$ $(x^{-5}y^{1/3})^{-3/5}$
Rewrite this expression as a fraction to change the sign of the exponent:
$(x^{-5}y^{1/3})^{-3/5}=\dfrac{1}{(x^{-5}y^{1/3})^{3/5}}=...$
Evaluate the power in the denominator and simplify:
$...=\dfrac{1}{x^{-3}y^{1/5}}=\dfrac{x^{3}}{y^{1/5}}=\dfrac{x^{3}}{\sqrt[5]{y}}$
$b)$ $(4r^{8}s^{-1/2})^{1/2}(32s^{-5/4})^{-1/5}$
Rewrite this expression as a fraction, to change the sign of the exponent of the second parentheses:
$(4r^{8}s^{-1/2})^{1/2}(32s^{-5/4})^{-1/5}=\dfrac{(4r^{8}s^{-1/2})^{1/2}}{(32s^{-5/4})^{1/5}}=...$
Evaluate the powers in the numerator and the denominator and simplify:
$...=\dfrac{(4^{1/2})r^{4}s^{-1/4}}{(32^{1/5})s^{-1/4}}=\dfrac{(\sqrt{4})r^{4}}{\sqrt[5]{32}}=\dfrac{2r^{4}}{2}=r^{4}$
