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priyankur just to let u knwo i figured out what we did wrong. we didnt square the original statement
5^(sqrt2) = 9.738 but then we have to square that to get 94.838

(5^1)^2 = 5^2 = 25 --> the answer is 5^2, not 25^2, which would equal 5^4 (incorrect).

(5^2)^2 = 5^{2*2} = 5^4 = 625 = 25^2 --> You see that we had to multiply the exponents (2*2) but didn't change the base at that stage yet. If we follow your logic we end up with 25^{2*2}, which is not right since we've squared the expression 5^2 twice, not once (we squared the base and multiplied the exponent by 2).

Let's see our problem again:

(5^{\sqrt{2}})^2 = 5^{2\sqrt{2}} = (5^2)^{\sqrt{2}} = 25^{\sqrt{2}} --> make sure you square the expression once

So, the right answer could be either 25^{\sqrt{2}} or 5^{2\sqrt{2}}. I hope it helped make it a bit clearer.

^^ what you did so far is correct. Further to match with the given choices, split 5^2*\sqrt{^2} as (5^2)\sqrt{^2} = (25)\sqrt{^2}, which is given in choices