There is no specific question as such. I am preparing for an aptitude exam, and am stuck at this particular point when we are required to find the last two digits/remainder when divided by 100 of an even number raised to a big power.

* $48^{277}$
* $86^{58}$
* $42^{79}$
* $74^{53}$

The above posted questions are just random ones, but are definitely part of my curriculum. the numbers cover even numbers ending in 2, 4, 6, 8. if anything else is required, please take any arbitrary example and help.