(1) 123 is divided by 4+3, so the last digits of 123rd power of 23, 1993 and 3123rd power are all the last digits of 7.

200 1 is divided by 4 and 1, so the last number of the power of 200 1993 is 3.

(2) Multiple digits ending in 5 or 6.

(3) The last number of 2004 to the power of 2005 is the last number of 1 to the power of 4, 4.

The last number of 2007 to the power of 2008 is the last number of 7 to the power of 4, 1.

The last number of 2008 to the power of 2007 is the last number of 8 to the power of 3, 2.