To find the numerical equivalent of \( 99 \cdot 9^{-6} \), we start by calculating \( 9^{-6} \).
Recall that \( 9^{-6} \) means \( \frac{1}{9^6} \).
Now, let's calculate \( 9^6 \):
\[ 9^6 = (9^3)^2 = 729^2 \]
Calculating \( 729^2 \):
\[ 729 \times 729 = 531441 \]
Thus, \( 9^6 = 531441 \), and therefore:
\[ 9^{-6} = \frac{1}{531441} \]
Next, we multiply \( 99 \) by \( 9^{-6} \):
\[ 99 \cdot 9^{-6} = 99 \cdot \frac{1}{531441} = \frac{99}{531441} \]
This means:
\[ 99 \cdot 9^{-6} = \frac{99}{531441} \]
Now, since you requested the answer without exponents, the numerical equivalent of \( 99 \cdot 9^{-6} \) is:
\[ \frac{99}{531441} \]
This fraction cannot be simplified further, so the final answer is:
\[ \frac{99}{531441} \]