Find the numerical equivalent of 9 rasied to the power of 9⋅9 rasied to the power of −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 properties of exponents.

We apply the property that states \( a^m \cdot a^n = a^{m+n} \):

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

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

\[ 9^{3} = 9 \cdot 9 \cdot 9 \]

Calculating this step-by-step:

1. First calculate \( 9 \cdot 9 = 81 \).
2. Then multiply the result by 9: \( 81 \cdot 9 \).

Now, calculating \( 81 \cdot 9 \):

\[ 81 \cdot 9 = 729 \]

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

\[ \boxed{729} \]