The unit's digit of the number 6^{256} - 4^{2 | vedclass

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(B) To find the unit's digit of $6^{256} - 4^{256}$,we analyze the cyclicity of the powers of $6$ and $4$.For any positive integer $n$,the unit's digi

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$0$

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(B) To find the unit's digit of $6^{256} - 4^{256}$,we analyze the cyclicity of the powers of $6$ and $4$.For any positive integer $n$,the unit's digit of $6^n$ is always $6$ because $6^1 = 6$,$6^2 = 36$,$6^3 = 216$,etc.For the powers of $4$,the unit's digit follows a cycle of length $2$: $4^1 = 4$,$4^2 = 16$ (unit digit $6$),$4^3 = 64$ (unit digit $4$),and so on.If the exponent is odd,the unit's digit is $4$. If the exponent is even,the unit's digit is $6$.Since $256$ is an even number,the unit's digit of $4^{256}$ is $6$.Therefore,the unit's digit of $6^{256} - 4^{256}$ is the unit's digit of $(6 - 6) = 0$.

The unit's digit of the number $6^{256} - 4^{256}$ is

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