\[\begin{array}{l}\frac{{{{15}^{\frac{2}{3}}} \cdot {3^{\frac{7}{3}}}}}{{{5^{ - \frac{1}{3}}}}} = \left[ {{{15}^{\frac{2}{3}}} = {3^{\frac{2}{3}}} \cdot {5^{\frac{2}{3}}}} \right] = \frac{{{5^{\frac{2}{3}}} \cdot {3^{\frac{2}{3}}} \cdot {3^{\frac{7}{3}}}}}{{{5^{ - \frac{1}{3}}}}} = \\\left[ {\frac{1}{{{5^{ - \frac{1}{3}}}}} = {5^{\frac{1}{3}}}} \right] = {5^{\frac{2}{3}}} \cdot {5^{\frac{1}{3}}} \cdot {3^{\frac{2}{3}}} \cdot {3^{\frac{7}{3}}} = {5^{\frac{2}{3} + \frac{1}{3}}} \cdot {3^{\frac{2}{3} + \frac{7}{3}}} = \\5 \cdot {3^3} = 5 \cdot 27 = 135\end{array}\]

\[135\]