\[\frac{x^{9}}{\left( x^{3} \right)^{4}} = \frac{x^{9}}{x^{12}} = x^{- 3};\]
\[x = \frac{2}{3}:\]
\[\left( \frac{2}{3} \right)^{- 3} = \left( \frac{3}{2} \right)^{3} = \frac{27}{8} = 3\frac{3}{8}.\]