What is the tens digit in 7 to the 2011th power?

Answer 1

71 = 7

72= 49

73 = 343

74 = 2401

75 = 16807

76 = 117649

The last two digits cycle after each exponent multiple of 4.

As 2011 = (4 x 502) + 3, then the tens digit in 72011 is the same as the tens digit in 73.......which is 4.

Answer 2

To find the tens digit in (7^{2011}), we need to consider the pattern of the last two digits of powers of 7. The units digit of powers of 7 cycles in the pattern 7, 9, 3, 1, and then repeats. The tens digit, however, follows a different pattern: 0, 0, 2, 4, 8, 6, 0, 0, 2, 4, 8, 6, and so on. Since 2011 is 3 more than a multiple of 4, the tens digit in (7^{2011}) will be 4.