Discussion

Explanation:

The last two digits of 25⁷⁷ are always 25.

Last two digits of 83⁴¹ = An even number   3 

i.e. ten's digit will be an even number and unit's digit will be 3.

Note: Tens digit of any power of a number, whose units digit is odd and tens digit is even, is always even.

Thus, the last two digits of 25⁷⁷ × 83⁴¹ will be given by 25 × a3 (where a is even).

Hence, 75.

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