1. Which of the numbers is greater: $77^{7}$ or $7^{77} ?$
Answer. The second number is greater.

Solution. $7^{10}>7^{2}>11$, therefore $7^{11}=7 \cdot 7^{10}>7 \cdot 11=77$. From this, it follows that $7^{77}=\left(7^{11}\right)^{7}>77^{7}$.

Grading criteria.

Correct answer and proof - 7 points.

Correct reasoning and incorrect answer at the end - 6 points.

Only answer - $\mathbf{1}$ point.