a)

$\frac{5^3\cdot {\left(5^2\right)}^3}{5^7}=\frac{5^3\cdot 5^6}{5^7}=\frac{5^{3+6}}{5^7}=\frac{5^9}{5^7}=5^{9-7}=5^2=25$

b)

$\frac{\sqrt{3}\cdot \sqrt{27}}{\sqrt[3]{108}:\sqrt[3]{4}}=\frac{\sqrt{3\cdot 27}}{\sqrt[3]{108:4}}=\frac{\sqrt{81}}{\sqrt[3]{27}}=\frac{9}{3}=3$