Puzzle of the Week #61 - Power Play

61 raised to the power of 61

or 61 61’s all multiplied together,

or 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61 x 61

is a very large number, with 109 digits altogether.

What are the last three digits?