What digit appears in the units place in the number obtained when [tex]2^{320}[/tex] is multiplied out?

Let's start with 2^x and see if we can find a recurring pattern to help us find the answer
2^1 = 2 2^2 = 4 2^3 = 8 2^4 = (1)6 2^5 = (3)2 2^6 = (6)4 2^7 = (12)8 2^8 = (25)6
If you notice, the pattern is 2,4,8,6 in the units place. Every four consecutive x's, the cycle repeats. So at 2^4, 2^8, 2^12 (4096), and 2^16(65336), the units place will all be 6, since x is always divisible by 4 here. When x= 320, we know that 320 is divisible by 4. This means that for 2^320, the units place will also be 6.
Hope this helps, even though it's rather vague!

Answered by cxcharlie | 2024-06-10

The units digit of 2 320 is 6 . This result comes from recognizing the repeating pattern of units digits in the powers of 2, which cycles every four terms as 2, 4, 8, 6. Since 320 is divisible by 4, it corresponds to the digit 6 in the cycle.
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Answered by cxcharlie | 2024-09-30