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Explanation:

Since 2 has a cyclicity of 4,
i.e. 21 = 2, 22 = 4, 23 = 8, 24 = 16, 25 = 32, 26 = 64 ..., the last digits (2, 4, 8, 6) are in four cycles.
∴ On dividing 514, we get the remainder as 3.

∴ The last digits has tobe 23 = 8

Shortcut:
Since cyclicity of the power of 2 is 4, so 251 can be written in 24(12) + 3 or unit digit will be 23 = 8.

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