Find the numerical equivalent of 9^9⋅9^−6 Your answer should be written without exponents

Answer 1

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

Thus, we have:

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

Next, we calculate \( 9^3 \):

\[ 9^3 = 9 \times 9 \times 9 \]

Calculating step by step:

1. \( 9 \times 9 = 81 \)
2. \( 81 \times 9 = 729 \)

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

\[ \boxed{729} \]