Alternate interpretation:
What is the units digit of 12^[13^(14¹�)]?
Determine the CYCLE of units digits when 12 is raised to increasing powers:
1
2¹ --> units digit of 2
1
2² --> units digit of 4
1
2³ --> units digit of 8
1
2� --> units digit of 6
1
2� --> units digit of 2
1
2� --> units digit of 4.
The results above indicate that the units digit repeat in a CYCLE OF 4:
2, 4, 8, 6...2, 4, 8, 6...2, 4, 8, 6...
Implication:
Every exponent that is a MULTIPLE OF 4 completes a cycle, yielding a UNITS DIGIT OF 6.
From there, the cycle REPEATS:
2, 4, 8...
Thus, every exponent that is ONE MORE THAN A MULTIPLE OF 4 begins a new cycle, yielding a UNITS DIGIT OF 2.
When 13 is raised to a power, the result = (multiple of 4) + 1.
13¹ = 13 = 12 + 1 = (4*1) + 1.
13² = 169 = 168 + 1 = (4*42) + 1.
13³ = 2197 = 2196 + 1 = (4*549) + 1.
Thus:
12^(13^power) = 12^(4a + 1), where a is a nonzero integer.
Since the exponent is one more than a multiple of 4, the units digit will be 2.
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