2. (7 points) Anya multiplied 20 twos, and Vanya multiplied 17 fives. Now they are going to multiply their huge numbers. What will be the sum of the digits of the product?
Answer: 8.

Solution. In total, 20 twos and 17 fives are multiplied. Let's rearrange the factors, alternating twos and fives. This results in 17 pairs of $2 \cdot 5$ and three additional twos, which multiply to 8. Thus, the number 8 needs to be multiplied by 10, 17 times. This results in a number consisting of the digit 8 followed by 17 zeros. The sum of the digits is 8. Another way to write the same reasoning using the properties of exponents is:

$$
2^{20} \cdot 5^{17}=2^{3} \cdot 2^{17} \cdot 5^{17}=8 \cdot(2 \cdot 5)^{17}=8 \cdot 10^{17}=800000000000000000 .
$$

## Grading Criteria.

- Any complete and correct solution - 7 points.
- Correct solution approach, correct product obtained, but the sum of digits not indicated - 5 points.
- Grouping of twos and fives into pairs that give tens, but the answer is not obtained or is incorrect - 2 points.