To evaluate \( 9^{-4} \), we can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \). Therefore, we have:
\[ 9^{-4} = \frac{1}{9^4} \]
Now, we need to calculate \( 9^4 \):
\[ 9^2 = 81 \]
So,
\[ 9^4 = 81^2 \]
Calculating \( 81^2 \):
\[ 81^2 = 6561 \]
Thus, \( 9^4 = 6561 \). Now we can substitute this back into our previous expression:
\[ 9^{-4} = \frac{1}{6561} \]
Therefore, the final answer is:
\[ \boxed{\frac{1}{6561}} \]