SOLUTION: what is the unit digit of 2^19? please give a detailed explanation because i still dont get after trying for an hour, thanks.

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
---------
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
---------
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?
:
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.

RELATED QUESTIONS
In a three digit number, the hundreds digit is equal to the tens digit, and is two more... (answered by josgarithmetic)

A boat that goes 12 miles per hour in still water takes as long to go 16 miles upstream... (answered by josgarithmetic,MathTherapy)

what is 5/6x = 30 + x ???????? i dont understand how to solve please explain in detail... (answered by Edwin McCravy)

Suppose that $7000 is invested at an interest rate of 5.8% per year, compounded... (answered by jirehcwe)

the largest 3 consecutive integers for which the first is increased by twice the second... (answered by ankor@dixie-net.com,MathTherapy)

I'm trying to help my daughter with her homework. We've finished it all, but I can't... (answered by josgarithmetic)

Which of the following is not 1/3 of an integer? F. -7 G. -1/3 H. 1 J. 1/3 K. (answered by stanbon)

1. one number is 2 more than 5 times the other. their product is 24 find the numbers how... (answered by josmiceli)

Hello! I am in need of an explanation for the following question I was assigned for... (answered by stanbon)