(C) Given the equation $(a^m)^n = a^{m^n}$.Using the law of exponents $(a^x)^y = a^{xy}$,we have $a^{mn} = a^{m^n}$.Equating the exponents,we get $mn

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(C) Given the equation $(a^m)^n = a^{m^n}$.Using the law of exponents $(a^x)^y = a^{xy}$,we have $a^{mn} = a^{m^n}$.Equating the exponents,we get $mn = m^n$.Dividing both sides by $m$ (assuming $m \neq 0$),we get $n = m^{n-1}$.Taking the $(n-1)$-th root on both sides,we get $m = n^{1/(n-1)}$.