9.053. $x^{2} \cdot 3^{x}-3^{x+1} \leq 0$.
Solution.

From the condition $x^{2} \cdot 3^{x}-3 \cdot 3^{x} \leq 0,3^{x}\left(x^{2}-3\right) \leq 0$. Since $3^{x}>0$ for $x \in R$, the obtained inequality is equivalent to the inequality $x^{2}-3 \leq 0$, $x^{2} \leq 3,-\sqrt{3} \leq x \leq \sqrt{3}$.

Answer: $\quad x \in[-\sqrt{3} ; \sqrt{3}]$