Question

If ${\left(a^m\right)}^n=a^{m^n}$ then 'm' =

Answer 1

Given $(a^m{)}^n=a^{m^n}$

$a^{mn}=a^{m^n}$

$⟹mn=m^n$

Applying logarithm on both sides

$⟹\log m+\log n=n\log m$

$⟹(n-1)\log m=\log n$

$⟹\log m=\frac{1}{n-1}\log n$

$⟹m=n^{1/(n-1)}$