22. (\frac{27}{4^{-1.5}})^{\frac{1}{3}}

$$(\frac{27}{4^{-1.5}})^{\frac{1}{3}} = (27 \cdot 4^{1.5})^{\frac{1}{3}} = (27 \cdot 4^{\frac{3}{2}})^{\frac{1}{3}} = (3^3 \cdot (2^2)^{\frac{3}{2}})^{\frac{1}{3}} = (3^3 \cdot 2^3)^{\frac{1}{3}} = (3 \cdot 2)^{\frac{3}{3}} = 6^{\frac{3}{3}} = 6^1 = 6$$