This question was previously asked in

SSB Head Constable 2018 Official Paper (Conducted on 3 Jan 2021)

Option 3 : 5^{100}

Given:

2250, 3150, 5100, 4200

Concept Used:

If a, b, c etc. are each > 1, then a^{x} > b^{x} > c^{x}, if a > b > c etc.

Calculation:

Let us change all the given numbers to the same index (power), in order to compare them.

The HCF of the powers 250, 150, 100 and 200 is 50.

2250 = 25×50 = (2^{5})^{50} = 32^{50}

3150 = 33×50 = (33)50 = 2750

5100, = 52×50 = (52)50 = 2550

4200. = 44×50 = (44)50 = 25650

It can be seen that 25^{50} = 5^{100} is the smallest.