Given the following expression:
[tex](8q^9)^{-4}[/tex]
To simplify the expression, we will use the following rules:
[tex]\begin{gathered} (a^m)^n=a^{m*n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]
So, the given expression will be as follows:
[tex](8q^9)^{-4}=8^{-4}*q^{9*-4}=\frac{1}{8^4}q^{-36}=\frac{1}{4096}q^{-36}[/tex]
So, the answer will be the second option
