Question 255255
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
So the fifth power of 7 ends with 7
7^2005 = (7^5)^401 
Therefore 7^2005 ends with 7.
So the one’s digit of the number 7^2005 is 7