7.062. $8^{\frac{x-3}{3 x-7}} \sqrt[3]{\sqrt{0.25^{\frac{3 x-1}{x-1}}}}=1$.
Solution.

Domain of definition $\left\{\begin{array}{l}x \neq 1, \\ x \neq \frac{7}{3} .\end{array}\right.$

Rewrite the equation as

$$
2^{\frac{3 x-9}{3 x-7}} \cdot 2^{-\frac{3 x-1}{3 x-3}}=2^{0}, 2^{\frac{3 x-9}{3 x-7}-\frac{3 x-1}{3 x-3}}=2^{0}
$$

from which

$$
\frac{3 x-9}{3 x-7}-\frac{3 x-1}{3 x-3}=0 \Rightarrow x=\frac{5}{3}
$$

Answer: $\frac{5}{3}$.