Discussion

Explanation:

The cyclicity of unit’s digit of powers of 7 is as follows:

7¹ = 7,
7² = 9,
7³ = 3,
7⁴ = 1,
7⁵ = 7,
7⁶ = 9,
7⁷ = 3,
7⁸ = 1,
…

Dividing 385 by 4 and the remainder is 1.

Thus, the last digit of 7³⁸⁵ is equal to the last digit of 7¹ i.e. 7.

Similarly, unit’s digit of 3²⁷⁸ = 3² = 9.

Therefore, unit’s digit of (7³⁸⁵ × 3²⁷⁸) is unit’s digit of product of digit at unit’s place of 7³⁸⁵ and 3²⁷⁸ = 1 × 9 = 9. 

Hence, 9.

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