To find the numerical equivalent of \( 9^9 \times 9^{-6} \), we can use the properties of exponents. Specifically, we can combine the exponents when the same base is being multiplied:
\[ 9^9 \times 9^{-6} = 9^{9 + (-6)} = 9^{9 - 6} = 9^3 \]
Now we need to calculate \( 9^3 \):
\[ 9^3 = 9 \times 9 \times 9 \]
Calculating this step by step:
- \( 9 \times 9 = 81 \)
- \( 81 \times 9 = 729 \)
Thus, the numerical equivalent of \( 9^9 \times 9^{-6} \) is
\[ \boxed{729} \]
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