Question

find the numerical equivalent of 9 to the 9th power times 9 to the -6 power

Answer 1

To find the numerical equivalent of \( 9^9 \times 9^{-6} \), we can use the properties of exponents. Specifically, when multiplying powers with the same base, we can add the exponents:

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

Now we can calculate \( 9^3 \):

\[
9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729
\]

Therefore, the numerical equivalent of \( 9^9 \times 9^{-6} \) is \( \boxed{729} \).