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

Answer 1

To solve for \( 9^9 \cdot 9^{-6} \), we can use the properties of exponents. In particular, we can use the rule that states \( a^m \cdot a^n = a^{m+n} \).

Here, we have:

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

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

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

Calculating this step-by-step:

1. Calculate \( 9 \cdot 9 = 81 \)
2. Then, calculate \( 81 \cdot 9 \):

\[ 81 \cdot 9 = 729 \]

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

\[ \boxed{729} \]