7.150. $\left(b^{\frac{\log _{100} a}{\lg a}} \cdot a^{\frac{\log _{100} b}{\lg b}}\right)^{2 \log _{a b}(a+b)}$.
Solution.

$$
\begin{aligned}
& \left(b^{\frac{\log _{100} a}{\lg a}} \cdot a^{\frac{\log _{100} b}{\lg b}}\right)^{2 \log _{a b}(a+b)}=\left(b^{\frac{1 \lg a}{2 \lg b}} \cdot a^{\frac{1 \lg ^{2} b}{2 \lg b}}\right)^{2 \log _{a b}(a+b)}= \\
& =\left((a b)^{\frac{1}{2}}\right)^{2 \log _{a b}(a+b)}=(a b)^{\log _{a b}(a+b)}=a+b
\end{aligned}
$$

Answer: $a+b$.