Use the properties of exponents to find the simplified expression:
[tex]\begin{gathered} \frac{m^2n^{\frac{5}{3}}\cdot m^{-\frac{1}{2}}n^{\frac{3}{4}}}{(mn^{\frac{3}{4}})^{\frac{1}{2}}\cdot m^{\frac{1}{2}}n^{\frac{3}{2}}} \\ \frac{m^{\frac{3}{2}}n^{\frac{29}{12}}^{}^{}}{(m^{\frac{1}{2}}n^{\frac{3}{8}})\cdot m^{\frac{1}{2}}n^{\frac{3}{2}}} \\ \frac{m^{\frac{3}{2}}n^{\frac{29}{12}}}{m^{}n^{\frac{15}{8}}^{}} \\ m^{\frac{1}{2}}n^{\frac{13}{24}} \end{gathered}[/tex]
The simplified expression is m^1/2 n^13/24
