(57242)^{9×7×5×3×1} = (57242)⁹⁴⁵

The unit digit of the resulting number is determined by the unit digit of the given number 57242, which is 2.

Reperation Cyclicity:

The cyclicity of the unit digit 2 is 4, resulting in the unit digit of the number being 2, 4, 8, or 6.

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16 (unit digit 6)

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2⁵ = 32 (unit digit 2)

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.

.

And so on.

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Now, 945 = 944 + 1.

944 is divisible by 4.

Hence, the last digit of (57242)⁹⁴⁵ will be the same as that of (57242)¹, which is 2.

Therefore, option (a) is the correct answer.