Question 164864
an interesting thing happens to the number as the exponent gets past 16.
the ones digit becomes 0 and stays 0 thereafter.
as you go up in exponent power, the number of 0's on the right hand side of the number keeps expanding.
for example: 
8^17 has one zero on the right (unit digit).
8^18 has 3 zeroes on the right (unit, ten, hundred digit).
8^22 has 5 zeroes on the right (unit, ten, hundred, thousand, ten thousand digit)
so, even though my calculator and my excel spreadsheet don't go up that far, i would assume the ones digit will remain 0 after 8^17. 
for a while (up to 8^11), the ones digit was repeating (8,4,2,6,8,4,2,6,8,4,2,6) and i was tempted to give you that answer but my curiosity got the best of me after my calculator threw up on 8^12 and i went to the excel spreadsheet.  it was there that i saw what was really happening.
here's a display of what the excel spreadsheet was telling me.
the first column is the number raised to the power in the second column.
----------------------------------------------------
x	:	8 raised to the power of x
----------------------------------------------------
1	:	8
2	:	64
3	:	512
4	:	4096
5	:	32768
6	:	262144
7	:	2097152
8	:	16777216
9	:	134217728
10	:	1073741824
11	:	8589934592
12	:	68719476736
13	:	549755813888
14	:	4398046511104
15	:	35184372088832
16	:	281474976710656
17	:	2251799813685250
18	:	18014398509482000
19	:	144115188075856000
20	:	1152921504606850000
21	:	9223372036854780000
22	:	73786976294838200000
23	:	590295810358706000000
24	:	4722366482869650000000
25	:	37778931862957200000000
26	:	302231454903657000000000
27	:	2417851639229260000000000
28	:	19342813113834100000000000
29	:	154742504910673000000000000
30	:	1237940039285380000000000000
31	:	9903520314283040000000000000
32	:	79228162514264300000000000000
33	:	633825300114115000000000000000
34	:	5070602400912920000000000000000
35	:	40564819207303300000000000000000
36	:	324518553658427000000000000000000
37	:	2596148429267410000000000000000000
38	:	20769187434139300000000000000000000
39	:	166153499473114000000000000000000000
40	:	1329227995784920000000000000000000000
-----------------------------------------------------------
i'm not sure what the algebraic answer to this would be.
i would supposes that after a certain amount of raising to a power for any number that the ones digit will eventually start being 0, but i don't know how to explain that other than it happens.  for example: 2 raised to the 50th power starts exhibiting the same thing, i.e. the ones digit becomes 0 and remains 0 thereafter.
a similarity in both these instances is that the number of digits other than 0 maxed at around 15.
did the same thing with 3 to the power of whatever and max number of digits before started getting 0's on the right appeared to be 15 as well.
i'm sure there's an explanation.
i just don't know it.
anyway, 0 is your answer to the best of my knowledge.