Which explanation correctly justifies why ${\left(a^m\right)}^n=a^{m\cdot n}$ using repeated multiplication?

It represents adding the base $a$ to itself $m$ times and then multiplying that sum by $n$.

It represents $n$ groups of $a^m$, meaning there are $n$ sets of $m$ factors of $a$, totaling $m\cdot n$ factors.

 It represents raising the inner exponent $m$ to the power of $n$, resulting in a new exponent of ^{$m^n$.}

It represents multiplying the base $a$ by the product of $m$ and $n$ because exponents always distribute over bases.