\sqrt[3]{ \frac{7}{4}}* \sqrt{ \frac{7}{4}}=(\frac{7}{4})^{\frac{1}{3}}*(\frac{7}{4})^{\frac{1}{2}}=(\frac{7}{4})^{\frac{2}{6}+\frac{3}{6}}=(\frac{7}{4})^{\frac{5}{6}}
{( \sqrt[3]{ \frac{7}{4}}* \sqrt{ \frac{7}{4}}) ^{ \frac{1}{4} }=[(\frac{7}{4})^{\frac{1}{3}}*(\frac{7}{4})^{\frac{1}{2}}]^{\frac{1}{4}}=[(\frac{7}{4})^{\frac{2}{6}+\frac{3}{6}}]^{\frac{1}{4}}=(\frac{7}{4})^{\frac{5}{6}*\frac{1}{4}}=(\frac{7}{4})^{\frac{5}{24}}}