3) $$ \sqrt[3]{\sqrt[3]{9}} \cdot \sqrt[3]{3\sqrt[3]{37}} = \sqrt[9]{3^2} \cdot \sqrt[3]{3 \cdot 3^{\frac{37}{3}}} = 3^{\frac{2}{9}} \cdot \sqrt[3]{3 \cdot 3^{\frac{37}{3}}} = 3^{\frac{2}{9}} \cdot \sqrt[3]{3^{\frac{40}{3}}} = 3^{\frac{2}{9}} \cdot 3^{\frac{40}{9}} = 3^{\frac{42}{9}} = 3^{\frac{14}{3}} $$
Ответ: $$3^{\frac{14}{3}}$$