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Question: If \((a^{m})^{n} = a^{m^{n}}\), then the value of 'm' in terms of 'n' is...

If (am)n=amn(a^{m})^{n} = a^{m^{n}}, then the value of 'm' in terms of 'n' is

A

n

B

n1/mn^{1/m}

C

n1/(n−1)n^{1/(n - 1)}

D

None of these

Answer

n1/(n−1)n^{1/(n - 1)}

Explanation

Solution

22+(2)2−2.22=2−2\sqrt{2^{2} + (\sqrt{2})^{2} - 2.2\sqrt{2}} = 2 - \sqrt{2}

⇒n=mn−1⇒m=n1n−1\Rightarrow n = m^{n - 1} \Rightarrow m = n^{\frac{1}{n - 1}}.