Find the last digit of (1008)2500.
Explanation:
Let’s look at the last digit of powers of 8.
81 = 8, 82 = 4, 83 = 2, 84 = 6, 85 = 8, 86 = 4, 87 = 2, 88 = 6, …
Thus, it can be seen that the unit’s digit of 8n is repeating after every 4 terms in the pattern of 8, 4, 2 and 6.
Hence, last digit of 84n+a will be same as the last digit of 8a.
i.e., to find the last digit, divide the required power by 4 and find the remainder.
So, when 2500 is divided by 4, it gives 0 as the remainder. Therefore, the last digit of 82500 is same as the last digit of 84 = 6.
Hence, option (b).
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