The given expression is:

$\frac{(9^{-8})^0}{9^{-4}}$

Step-by-step solution:

1. Simplify $(9^{-8})^0$: Any non-zero number raised to the power of 0 equals 1. So: $(9^{-8})^0 = 1$

   Now the expression becomes: $\frac{1}{9^{-4}}$

2. Simplify the denominator $9^{-4}$: Using the negative exponent rule, $a^{-n} = \frac{1}{a^n}$, we can rewrite $9^{-4}$ as: $9^{-4} = \frac{1}{9^4}$

   So the expression now is: $\frac{1}{\frac{1}{9^4}} = 9^4$

Final answer:

$9^4 = 6561$

So, the value of the given expression is 6561.

Would you like more details or have any further questions?

Here are some related questions for further practice:

1. Simplify $\frac{(5^{-3})^0}{5^{-2}}$.
2. Simplify $\frac{(7^{-5})^2}{7^{-3}}$.
3. What is $\frac{(2^3)^0}{2^{-2}}$?
4. Evaluate $\frac{(10^{-2})^0}{10^{-1}}$.
5. Simplify $\frac{(3^{-6})^0}{3^{-5}}$.

Tip: Any base (except 0) raised to the power of 0 always equals 1!