a)

$\frac{\sqrt{75}\cdot \sqrt{3}-\sqrt{45}:\sqrt{5}}{\sqrt{2}\cdot \sqrt{18}}=\frac{\sqrt{75\cdot 3}-\sqrt{45:5}}{\sqrt{2\cdot 18}}=\frac{\sqrt{225}-\sqrt{9}}{\sqrt{36}}=\frac{15-3}{6}=\frac{12}{6}=2$

b)

$\sqrt[3]{2\frac{1}{8}}\cdot \sqrt{5\frac{2}{3}}\cdot \sqrt[3]{\frac{8}{17}}\cdot \sqrt{\frac{3}{17}}=\sqrt[3]{2\frac{1}{8}}\cdot \sqrt[3]{\frac{8}{17}}\cdot \sqrt{5\frac{2}{3}}\cdot \sqrt{\frac{3}{17}}=$ $\sqrt[3]{2\frac{1}{8}\cdot \frac{8}{17}}\cdot \sqrt{5\frac{2}{3}\cdot \frac{3}{17}}=$  

$=\sqrt[3]{\frac{{\sout{17}}^1}{{\sout{8}}^1}\cdot \frac{{\sout{8}}^1}{{\sout{17}}^1}}\cdot \sqrt{\frac{{\sout{17}}^1}{{\sout{3}}^1}\cdot \frac{{\sout{3}}^1}{{\sout{17}}^1}}=\sqrt[3]{1}\cdot \sqrt{1}=1\cdot 1=1$