Решение:

1. a) $$\sqrt[3]{\frac{3^9}{0{,}125}} = \sqrt[3]{\frac{3^9}{\frac{1}{8}}} = \sqrt[3]{3^9 \cdot 8} = \sqrt[3]{3^9 \cdot 2^3} = 3^{\frac{9}{3}} \cdot 2^{\frac{3}{3}} = 3^3 \cdot 2 = 27 \cdot 2 = 54$$
2. б) $$\sqrt[4]{3^8 \cdot 2^4} = 3^{\frac{8}{4}} \cdot 2^{\frac{4}{4}} = 3^2 \cdot 2 = 9 \cdot 2 = 18$$
3. в) $$\sqrt[8]{\frac{2^8 \cdot 3^{24}}{5^{16}}} = \frac{2^{\frac{8}{8}} \cdot 3^{\frac{24}{8}}}{5^{\frac{16}{8}}} = \frac{2 \cdot 3^3}{5^2} = \frac{2 \cdot 27}{25} = \frac{54}{25} = 2{,}16$$

Ответ: а) 54; б) 18; в) 2,16.