Defining L(G) in set notation
They are not all equivalent.

Strings in the expression $(a^nb^n)^k$ have several (i.e., $k$) copies of the same string $a^nb^n$, whereas in $a^{n_1}b^{n_1}\dots a^{n_k}b^{n_k}$ the number of letters in each $a^{n_i}b^{n_i}$ may differ.

As $aaabbbaaabbbaaabbb$ versus $aabbaaaabbbbab$.

A shorter way of denoting words with different numbers would be
$\{ a^nb^n \mid n\ge0\}^*$.

Now check out your three languages and the given grammar.