What is the last digit of 7 to the power of 2007? the logical thing to do would be to work out a pattern. does anyone have and pointers about which direction I should go in.

i guess you answered the question yourself.. yes you have to derive a pattern
7^
0=1
1=7
2=49
3=343
4=2401
5=16807

you do not need to even write any other digit except the units digit.
its like this..
abjhbajsa7
x7
_________
tytiyqoiywt9

the units digit on one stage would produce the units digit of the next stage. the result would be independant of any other digit.
now.. as you saw.. the pattern is a set of 4's. every power which is of the form 4n+1 gives 7..4n+2 gives 9.. 4n+3 gives 3 and 4n+0 = 1

2007 mod 4 = 3
2004+3 = 4n + 3
so the units digit is 3

i hope i am right