Question

Find the numerical equivalent of 9 to the power of 9 ⋅ 9 to the power of −6
. Your answer should be written without exponents. (1 point)

Answer 1

To find the numerical equivalent of \( 9^9 \cdot 9^{-6} \), we can use the exponent rule that states \( a^m \cdot a^n = a^{m+n} \).

Applying this rule:

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

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

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

Calculating this step-by-step:

\[
9 \times 9 = 81
\]
\[
81 \times 9 = 729
\]

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

\[
\boxed{729}
\]