If \( \Large a^{m^{n}}= \left(a^{m}\right)^{n} \), then the value of m is

A) n

B) \( \Large \frac{n}{n^{n-1}} \)

C) \( \Large \frac{1}{n^{n-1}} \)

D) \( \Large n^{\frac{n-1}{n}} \)

Correct answer:
C) \( \Large \frac{1}{n^{n-1}} \)

Description for Correct answer:

Given: \( \Large a^{m^{n}} = \left(a^{m}\right)^{n} = a^{m \times n} \)

\( \Large \therefore m^{n} = mn \)

\( \Large m^{n-1} = n \)

\( \Large \therefore m = n^{\frac{1}{n-1}} \)



Please provide the error details in above question