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Q. If \( \sqrt{5^n} = 125 \), find \( 5^{\sqrt[n]{64}} \)
(a) 25 (b) \( \frac{1}{125} \) (c) 625 (d) \( \frac{1}{5} \)
✏️ Solution
\( (5^n)^{1/2} = 125 = 5^3 \)
\( 5^{n/2} = 5^3 \Rightarrow n = 6 \)
\( \sqrt[6]{64} = (2^6)^{1/6} = 2 \)
\( 5^{\sqrt[n]{64}} = 5^2 = 25 \)
Correct Option: (a) 25
\( \boxed{25} \)