Discussion

Explanation:

Let’s look at the last digit of powers of 3.

3¹ = 3,
3² = 9,
3³ = 7,
3⁴ = 1, 
3⁵ = 3, 
3⁶ = 9,
3⁷ = 7,
3⁸ = 1,
… 

Thus, it can be seen that the unit’s digit of 3ⁿ is repeating after every 4 terms in the pattern of 3, 9, 7 and 1.

Hence, last digit of 3^4n+a will be same as the last digit of 3^a.

i.e., to find the last digit, divide the required power by 4 and find the remainder. 

So, unit’s digit of (173)⁹⁹ will be units digit of 3⁹⁹, which be same as unit’s digit of 3^4×24+3 = 3³ = 7.

Hence, option (b).

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