What is the unit’s digit in the expansion of 2 raised to 725?

Answer 1

The unit's digit in the expansion of 2 raised to the 725th power is 8. This can be determined by using the concept of the "unit's digit law". This law states that the units digit of a number raised to any power is the same as the units digit of the number itself. In this case, the number is 2, which has a units digit of 2, so the units digit of 2 to the 725th power is also 2.

However, this is not the final answer. To get the unit's digit of 2 to the 725th power, we must use the "repeating pattern law". This law states that when a number is raised to any power, the unit's digit will follow a repeating pattern. For 2, this pattern is 8, 4, 2, 6. This means that the units digit of 2 to any power will follow this pattern, repeating every 4 powers.

So, if we look at the 725th power of 2, we can see that it is in the 4th cycle of this repeating pattern. This means that the units digit of 2 to the 725th power is 8.