Observe the following formulas: 3 ^ 1 = 3, 3 ^ 2 = 9, 3 ^ 3 = 27, 3 ^ 4 = 81, 3 ^ 5 = 243, 3 ^ 6 = 729 (1) Do you find any regularity in their single digit numbers? (2) What is the number of 3 ^ 2007 based on your findings

3 ^ 1 = 3, one bit is 3
3 ^ 2 = 9, the number of bits is 9
3 ^ 3 = 27, bits are 7
3 ^ 4 = 81, one bit is 1
3 ^ 5 = 243, the number of bits is 3
3 ^ 6 = 729, the number of bits is 9
The fifth power and the first power are the same
The power of 6 is the same as the power of 2
……
So it's a cycle of four
2007=4*501+3
So 3 ^ 2007 bits is the same as 3 ^ 3 bits
So 3 ^ 2007 bits is 7

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