Expand ${(-4b)}^7$ and write in exponent form.

As we know for any non-zero integers $\text{'}a\text{'}$ and $\text{'}b\text{'}$ and for any natural number $\text{'}n\text{'}$, $a^n\times b^n={\left(a\times b\right)}^n$.

So, ${(-4b)}^7$ is in the form of ${(a\times b)}^n$ only, thus, we can write exponent individually on each base, i.e., ${(-4b)}^7$$={(-4)}^7\times b^7$.

Hence, ${(-4b)}^7$$={(-4)}^7\times b^7$ in the expanded form.