Question 657007: what is the unit digit of 2^19? please give a detailed explanation because i still dont get after trying for an hour, thanks.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! what is the unit digit of 2^19?
:
A pattern can be demonstrated here
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
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2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
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You notice the units are a repeating series, 2,4,8,6 and this will repeat no
matter how high the exponents go
So we can say that every exponent that is a multiple of 4 will have unit of 6
Then the 2,4,8,6 series begins again
:
In our problem, 2^19, we know 2^16 has a unit of 6, start series from there
2,4,8, 2^19 has a unit of 8, right?
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Another words
2^20, 20 is a multiple of 4, so it will have a unit of 6, therefore going back
one in the series to 2^19, it would be 8, right
:
YOu can find the unit value of any exponent of 2 this way.
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