Find the units digit of (128)^{182} ? | vedclass

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Question

(B) The unit digit of $(128)^{182}$ is the same as the unit digit of $8^{182}$.Powers of $8$ follow a cyclicity of $4$ for their unit digits: $8^1 = 8

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The unit digit of $(128)^{182}$ is the same as the unit digit of $8^{182}$.Powers of $8$ follow a cyclicity of $4$ for their unit digits: $8^1 = 8$,$8^2 = 64$ (unit digit $4$),$8^3 = 512$ (unit digit $2$),$8^4 = 4096$ (unit digit $6$),and $8^5$ returns to $8$.The cycle is $(8, 4, 2, 6)$.Divide the exponent $182$ by the cycle length $4$: $182 = 4 	imes 45 + 2$.The remainder is $2$.Therefore,the unit digit of $(128)^{182}$ is the same as the unit digit of $8^2$,which is $4$.

Find the units digit of $(128)^{182} ?$

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