SOLUTION: what are the last two digits of the number {{{ 7^8910 }}} when it is fully calculated out?

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Question 1191159: what are the last two digits of the number +7%5E8910+ when it is fully calculated out?
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


The sequence of the last two digits of increasing powers of 7 will form a repeating pattern. Use the length of that pattern to find the answer.

07
49
43
01
07
....

That is a very short pattern with length 4.

The exponent 8910, divided by 4, leaves remainder 2, so the answer is the 2nd number in the repeating pattern: 49

ANSWER: 49