7.146. $\left\{\begin{array}{l}\log _{\sqrt{x}}(x y)=8 \\ \log _{3} \log _{1 / 9} \frac{x}{y}=0 .\end{array}\right.$

The system of equations is:
\[
\left\{\begin{array}{l}
\log _{\sqrt{x}}(x y)=8 \\ 
\log _{3} \log _{1 / 9} \frac{x}{y}=0 .
\end{array}\right.
\]
Solution.

Odz: $\left\{\begin{array}{l}00, \\ \log _{1 / 9} \frac{x}{y}>0 \Rightarrow 0<\frac{x}{y}<1 .\end{array}\right.$

From the first equation of the system $x y=x^{4}$ or considering the domain of definition (ODZ) $y=x^{3}$. From the second equation we have $\log _{1 / 9} \frac{x}{y}=1, \frac{x}{y}=\frac{1}{9}$. The original system can be rewritten as $\left\{\begin{array}{l}y=x^{3}, \\ \frac{x}{y}=\frac{1}{9}\end{array} \Rightarrow \frac{x}{x^{3}}=\frac{1}{9}\right.$, from which, considering the ODZ, $x=3, y=27$.

Answer: $(3 ; 27)$.