Is this concatenation ({a} · {b})^2 ≠ a^2 · b^2?
They are different, because:
$(a \cdot b)^2 = abab$, since you need to concatenate $a$ and $b$ first, them reapeat the concatenation two times.
$a^2 \cdot b^2 = aabb$, since you need to concatenate the repetition of two $a$ with the repetition of two $b$.