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Look at the first few powers of 2: 2, 4, 8, 16, 32, 64, 128, 256,512, 1024, 2048

The units digit repeats every four: [ 2 - 4 - 8 - 6 ] - [ 2 - 4 - 8 - 6 ] - etc.

725/4 = 181 with remainder of 1 .

So if you raise 2 to the 725th power, the units digit completes the whole

4-step cycle [ 2-4-8-6 ] 181 times, and then advances one more step ... to 2 .

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Q: What is the units digit of 2 to the 725th power?
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What is the unit’s digit in the expansion of 2 raised to 725?

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.


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