What is the last number to the 2008 power of 3?

What is the last number to the 2008 power of 3?

1
The power of 3 is 3,9,7,1,3,9,7,1
So every four groups.
2008=4*502
So the last number is 1.

The end of the 2008 power of 2 is

The first power bit of 2 is 2
2Th power of 2=4, bits are 4
The third power of 2=8, the bits are 8
4Th power of 2=16, bits are 6
The fifth power of 2=32, the bits are 2
Same as 1st power of 2
So it's four cycles.
2008÷4 Remainder is 0
That is, the remainder is 4.
So it's the same as the fourth power of 2
So a mantissa to the 2008 power of 2 is 6

The first power bit of 2 is 2
2Th power of 2=4, bits are 4
The third power of 2=8, the bits are 8
4Th power of 2=16, bits are 6
The fifth power of 2=32, bits are 2
Same as 1st power of 2
So four cycles.
2008÷4 Remainder is 0
That is, the remainder is 4.
So it's the same as the fourth power of 2
So a mantissa to the 2008 power of 2 is 6