$a)\frac{a^3\cdot \sqrt[5]{b^2}\cdot c^4\cdot d\cdot \sqrt[3]{e^2}}{b^4\cdot \sqrt{d}}=\frac{a^3\cdot b^{\frac{2}{5}}\cdot c^4\cdot d\cdot e^{\frac{2}{3}}}{b^4\cdot d^{\frac{1}{2}}}=a^3\cdot b^{\frac{2}{5}-4}\cdot c^4\cdot d^{1-\frac{1}{2}}\cdot e^{\frac{2}{3}}=a^3\cdot b^{-\frac{18}{5}}\cdot c^4\cdot d^{\frac{1}{2}}\cdot e^{\frac{2}{3}}$

$b)\frac{\sqrt[3]{x}\cdot \sqrt[5]{y^2}\cdot \sqrt[4]{z^3}}{x^2\cdot z^4}=\frac{x^{\frac{1}{3}}\cdot y^{\frac{2}{5}}\cdot z^{\frac{3}{4}}}{x^2\cdot z^4}=x^{\frac{1}{3}-2}\cdot y^{\frac{2}{5}}\cdot z^{\frac{3}{4}-4}=x^{-\frac{5}{3}}\cdot y^{\frac{2}{5}}\cdot z^{-\frac{13}{4}}$