SOLUTION: what is the ones (or unit) digit in 2^4000

Algebra.Com
Question 783195: what is the ones (or unit) digit in 2^4000
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
210 = 1024
211 = 2048
212 = 4096
213 = 8192
214 = 16384
215 = 32768
216 = 65536

As you can see the units digits go 2,4,8,6,2,4,8,6,...

Every time the exponent to which 2 is raised is a 
multiple of 4, the units digit is a 6.

Therefore since 4000 is a multiple of 4,

24000 has units digit 6.

Edwin
RELATED QUESTIONS

what is the ones or unit digit for 9^34... (answered by MathLover1,Alan3354)
how many 2-digit prime numbers have 3 or 7 in the ones... (answered by richard1234)
I am a four digit number greater than 3000 but less than 4000. My ones digit is 2 more... (answered by ewatrrr)
i am a four digit number greater than 3000 but less than 4000. My ones digit is 2 more... (answered by ewatrrr)
what is the digit in the unit place... (answered by Alan3354,Edwin McCravy)
In a three digit number, the sum of its ones digit and tens digit is ten. Its tens digit... (answered by Edwin McCravy)
I am a number between 4000 and 5000. My ones digit is 3 less than 9, my tens digit is... (answered by rmcaz79,ankor@dixie-net.com)
what is the unit digit in (2657)^2004... (answered by checkley71)
In a 4-digit number the tens and hundreds digits are 3. The ones digit is twice the tens... (answered by Edwin McCravy)