It does not matter how many times 6 is multiplied by 6. The unit's digit is always 6 (unless x is 0 or -ve).
Hence , Units digit of both \(6^x\) & \(6^{(x−1)}\) is \(6\).
Hence after subtraction the units digit is 0.
Hence , I would go for option A.
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Solution

Given:
• The value of the integer x is greater than 1

To find:
• The unit digit of the expression \(6^x\) – \(6^{(x-1)}\)

Approach and Working:
• If we observe the unit digit pattern of 6, we can see for any positive power of 6, the number will always end with 6 only

o \(6^1\) = 6
o \(6^2\) = 36
o \(6^3\) = 216 etc.

• As x > 1, x-1 > 0

o Hence, \(6^x\) and \(6^{(x-1)}\) will always end with the unit digit 6

• Therefore, \(6^x\) - \(6^{(x-1)}\) will end with 0
Hence, the correct answer is option A.

Answer: A
_________________

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