what will be last digit of((2002)^2008) + ((2008)^2002)

To find the last digit, we look at the units digit of each term. Numbers ending in 2 raised to any power have a cyclical pattern for the units digit: 2, 4, 8, 6 repeating every 4 powers. For 2002^2008, we check 2008 mod 4 = 0, so the units digit is 6. For 2008^2002, we check 2002 mod 4 = 2, so the units digit is 4. Adding: 6 + 4 = 10, which has a last digit of 0.