Find the numerical equivalent of 9^9⋅9^−6

Question

. Your answer should be written without exponents. (1 point)

Answer 1

To solve \( 9^9 \cdot 9^{-6} \), we can use the property of exponents, which states that \( a^m \cdot a^n = a^{m+n} \).

Applying that property:

\[ 9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{9 - 6} = 9^3. \]

Now, we need to calculate \( 9^3 \):

\[ 9^3 = 9 \cdot 9 \cdot 9 = 81 \cdot 9 = 729. \]

Therefore, the numerical equivalent of \( 9^9 \cdot 9^{-6} \) is \(\boxed{729}\).