\frac{81\sqrt[3]3}{\sqrt{27}}=3^{x^2}
\frac{3^4*3^{\frac{1}{3}}}{\sqrt{3^3}}=3^{x^2}
\frac{3^{4\frac{1}{3}}}{3^{\frac{3}{2}}}=3^{x^2}
3^{\frac{13}{3}-\frac{3}{2}}=3^{x^2}
3^{\frac{26}{6}-\frac{9}{6}}=3^{x^2}
3^{\frac{17}{6}}=3^{x^2}
x^2=\frac{17}{6}
x_1=-\sqrt{\frac{17}{6}}=-\frac{\sqrt{17}}{\sqrt6}=-\frac{\sqrt{17}*\sqrt6}{\sqrt6*\sqrt6}=-\frac{\sqrt{102}}{6}
x_2=\sqrt{\frac{17}{6}}=\frac{\sqrt{102}}{6}