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

Question

. Your answer should be written without exponents

Answer 1

To simplify the expression \( 9^9 \cdot 9^{-6} \), we can 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. \( 81 \times 9 = 729 \)

Therefore, \( 9^3 = 729 \).

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