find the numerical equivalent of 9^9 • 9^-6. your answer should be written without exponents

Answer 1

To find the numerical equivalent of \( 9^9 \cdot 9^{-6} \), 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 \( 9^3 \):

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

First, calculate \( 9 \times 9 \):

\[ 9 \times 9 = 81 \]

Next, multiply by 9 again:

\[ 81 \times 9 = 729 \]

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

\[ \boxed{729} \]