Is this concatenation ({a} · {b})^2 ≠ a^2 · b^2? I presumed they were equal, such that both resulted in aabb. However, I'm told they are false and I don't know why.
Is it because in the second one, we would concatenate a · b before raising to the power of 2, thus resulting in abababab? Or because in the first one you concatenate first, thus resulting in abab?
Thanks in advance.
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 $b$.