1. (7 points) Compare $3^{76}$ and $5^{50}$.
Solution. $3^{76}=3^{4} \cdot 3^{72}=81 \cdot\left(3^{3}\right)^{24}=81 \cdot(27)^{24}$.

$5^{50}=5^{2} \cdot 5^{48}=25 \cdot\left(5^{2}\right)^{24}=25 \cdot(25)^{24}$.

Since $81>25$ and $27>25$, then $3^{76}>5^{50}$.

Answer. $3^{76}>5^{50}$.