Discussion

Explanation:

Now, 54³⁸⁰ = 2³⁸⁰ × 27³⁸⁰

Last two digits of 2³⁸⁰ = 2^10×38 = 76.

Last two digits of 27³⁸⁰ = Last two digits of (3³)³⁸⁰
= Last two digits of (3)¹¹⁴⁰
= Last two digits of (3⁴)²⁸⁵
= Last two digits of (81)²⁸⁵
= 01

∴ Last two digits of 54³⁸⁰ = last two digits of (2³⁸⁰) × last two digits of (27³⁸⁰) = 76 × 01 = 76.

Hence, 76.

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