If $a^{m^n}=(a^m{)}^n$, then the value of $m$ is

1. Simplify the right side using the laws of exponents, $(a^m{)}^n=a^{m\cdot n}$:
$$a^{m^n}=a^{m\cdot n}$$
Since the bases are identical ($a$), equate their exponents:
$$m^n=m\cdot n$$
Divide both sides by $m$ (which is equivalent to $m^1$):
$$\frac{m^n}{m^1}=n$$
$$m^{n-1}=n$$
Solve for $m$ by taking the $(n-1)$ -th root of both sides:
$$m=n^{\frac{1}{n-1}}$$