Evaluate

limx0e3x31+3x392x614x9\displaystyle \lim_{{{x}\to{0}}}{\frac{{{e}^{{-{3}{x}^{{3}}}}-{1}+{3}{x}^{{3}}-{\frac{{{9}}}{{{2}}}}{x}^{{6}}}}{{{14}{x}^{{9}}}}}

Hint: Using power series.