[tex]\dfrac{2^5 \cdot \sqrt[3]{16} }{8 \cdot \dfrac{1}{4}} = \\\\\\\dfrac{2^5 \cdot \sqrt[3]{2^4}}{2^3\cdot \dfrac{1}{2^2}} = \\\\\\\dfrac{2^5 \cdot 2^{\frac{3}{4}}}{2^3 \cdot 2^{-2}} = \\\\\\\dfrac{2^{\frac{20+3}{4}}}{2^{(3-2)}} = \dfrac{2^{\frac{23}{4}}}{2} = 2^{\frac{23}{4}-1} = 2^{\frac{23-4}{4}} = 2^{\frac{19}{4}}[/tex]