［Solution］The original equation is
$$\begin{aligned} 3 \cdot 3^{x^{2}}+\frac{1}{3} \cdot 3^{x^{2}}-270 & =0, \\ 10 \cdot 3^{x^{2}} & =810, \\ 3^{x^{2}} & =3^{4}, \\ x^{2} & =4, \\ x & = \pm 2 . \end{aligned}$$

Upon verification, $x= \pm 2$ are solutions to the original equation.