((2/5)3/8)^1/2 × ((2/5)^1/4)^1/2 ______________________ = (2/5)^3/16

[tex] = \frac{ { \frac{2}{5} }^{ \frac{3}{8} \times \frac{1}{2} } \times{ \frac{2}{5} }^{ \frac{1}{4} \times \frac{1}{2} } }{ { \frac{2}{5} }^{ \frac{3}{16} } } \\ = \frac{ { \frac{2}{5} }^{ \frac{3}{16} } \times { \frac{2}{5} }^{ \frac{1}{8} } }{{ \frac{2}{5} }^{ \frac{3}{16} }} \\ = { \frac{2}{5} }^{ \frac{3}{16} + \frac{3}{16} - \frac{1}{8} } \\ = { \frac{2}{5} }^{ \frac{1}{8} } = \sqrt[8]{ \frac{2}{5} } [/tex]