To find the numerical equivalent of \( 9^9 \cdot 9^{-6} \), we can use the properties of exponents.
The property states that: \[ a^m \cdot a^n = a^{m+n} \]
Applying this property here:
\[ 9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{9 - 6} = 9^3 \]
Now, we need to calculate \( 9^3 \):
\[ 9^3 = 9 \times 9 \times 9 \]
Calculating it step by step:
\[ 9 \times 9 = 81 \]
Then multiplying by 9 again:
\[ 81 \times 9 = 729 \]
Thus, the numerical equivalent of \( 9^9 \cdot 9^{-6} \) is \( 729 \).
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