Answer
128i
Work Step by Step
Here, we are using the pattern of squaring i.
For example, $i^{1}=i$, $i^{2}=-1$, $i^{3}=-1\times i=-i$, $i^{4}=-i\times i=-i^{2}=-1\times-1=1$, and so on.
Therefore, we can use the fact that $i^{4}=1$ and then rewrite the expression in terms of $i^{4}$ in order to simplify.
$(-2i)^{7}=(-2)^{7}i^{7}=-128(i^{4}\times i^{3})=-128(1\times -i)=-128(-i)=128i$