4. Six numbers are written in a row on the board. It is known that each number, starting from the third, is equal to the product of the two preceding numbers, and the fifth number is equal to 108. Find the product of all six numbers in this row.
4. Answer: 136048896.

Solution. Let the first number be $x$, and the second number be $y$. Then the third number is $xy$.

The fourth number is $xy^2$. The fifth number is $x^2 y^3 = 108$. The sixth number is $x^3 y^3$.

The product of all six numbers is $x^8 y^{12} = (x^2 y^3)^4 = 108^4 = 136048896$.

## Grading Criteria.

A specific case is considered - a sequence where the first number is 2 and the second number is 3: 1 point.

Comment. Other sequences also work, for example, a sequence with the first number (-2) and the second number 3.

The answer $108^4$ is derived correctly but not calculated or calculated incorrectly: 6 points.