请教大家多次方求余数的题应怎样做

Which of the following us the last two digits of 7⁹⁴⁶?

A)17    B) 29    C) 49   D) 31  E) 43

Key  C

请教大家这类求余数的题应怎样做， 多谢！

Which of the following us the last two digits of 7⁹⁴⁶?

A)17    B) 29    C) 49   D) 31  E) 43

Key  C

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My thought:

Sorry I don't have Chinese word processer right now on hand, so I have to type English.

Look for the rule first by listing first few numbers:

1) 7^1 = 7

2) 7^2=49

3) 7^3=343

4) 7^4=2401

5) 7^5=***07, 7 again.

...

So the last two digits of 7 to the power of 1,2,3,4... will be 07, 49, 43, 01..., four in a cycle.

Then 946/4=236 remaider is 2. So 49 is the right answer.