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

Question

. Your answer should be written without exponents.

Answer 1

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

Applying this property:

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

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

\[ 9^3 = 9 \times 9 \times 9 \] Calculating step by step:

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

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

\[ \boxed{729} \]