To find the numerical equivalent of \( 99 \cdot 9^{-6} \), we can first rewrite \( 9^{-6} \) as \( \frac{1}{9^6} \).
So, we have:
\[ 99 \cdot 9^{-6} = 99 \cdot \frac{1}{9^6} = \frac{99}{9^6} \]
Next, we need to calculate \( 9^6 \):
\[ 9^6 = (3^2)^6 = 3^{12} \]
Calculating \( 3^{12} \):
\[ 3^{12} = 531441 \]
Now substituting this back in, we get:
\[ 99 \cdot 9^{-6} = \frac{99}{531441} \]
Thus, the numerical equivalent of \( 99 \cdot 9^{-6} \) is:
\[ \frac{99}{531441} \]
If you want to express it as a decimal, you can compute:
\[ 99 \div 531441 \approx 0.000186 \]
However, the answer in fractional form is:
\[ \frac{99}{531441} \]
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