Let's analyze the given equation [tex]\(3^{-8} = 9^{-4}\)[/tex] step by step:
1. Start with the expression [tex]\(9^{-4}\)[/tex].
2. Rewrite 9 as [tex]\(3^2\)[/tex] because [tex]\(9\)[/tex] is the same as [tex]\(3\)[/tex] squared.
3. So, [tex]\(9^{-4}\)[/tex] can be rewritten as [tex]\((3^2)^{-4}\)[/tex].
4. Applying the power of a power property, [tex]\((a^m)^n = a^{m \cdot n}\)[/tex], we get [tex]\((3^2)^{-4} = 3^{2 \cdot (-4)} = 3^{-8}\)[/tex].
5. Now, the original equation [tex]\(3^{-8} = 9^{-4}\)[/tex] can be rewritten as [tex]\(3^{-8} = 3^{-8}\)[/tex], which is evidently True.
Therefore, the correct answer is:
[tex]\[\boxed{\text{True}}\][/tex]
