Example 5. Solve the inequality

$$
3^{72}\left(\frac{1}{3}\right)^{x}\left(\frac{1}{3}\right)^{V \bar{x}}>1
$$
Solution. The domain of the inequality is $x \geqslant 0$. By reducing the left part of the inequality to a power with base 3, we get

$$
3^{72}\left(\frac{1}{3}\right)^{x}\left(\frac{1}{3}\right)^{\sqrt{x}}=3^{72-x-\sqrt{x}}
$$

Thus, the given inequality is equivalent to the inequality

$$
72-x-\sqrt{x}>0
$$

Let $t=\sqrt{x};$ we have:

$$
\left\{\begin{array} { l } 
{ t \geqslant 0 } \\
{ t ^ { 2 } + t - 7 2 < 0 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
t \geqslant 0 \\
(t+9)(t-8)<0
\end{array} \Leftrightarrow 0 \leqslant t<8\right.\right.
$$

Thus, the given inequality is equivalent to the double inequality

$$
0 \leqslant \sqrt{x}<8
$$

from which $0 \leqslant x<64$.

Therefore, the interval $[0 ; 64)$ is the set of all solutions to the given inequality.