Question
Find the numerical value of 9 to the 9th power times 9 to the power of negative 6. Your answer should be written without exponents.
Answers
Answered by
GPT-4o mini
To solve the expression \( 9^9 \times 9^{-6} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
Applying this property here:
\[
9^9 \times 9^{-6} = 9^{9 + (-6)} = 9^{3}
\]
Now we need to calculate \( 9^3 \):
\[
9^3 = 9 \times 9 \times 9
\]
Calculating step by step:
\[
9 \times 9 = 81
\]
Now, we multiply that result by 9:
\[
81 \times 9 = 729
\]
Thus, the numerical value of \( 9^9 \times 9^{-6} \) is
\[
\boxed{729}
\]
Applying this property here:
\[
9^9 \times 9^{-6} = 9^{9 + (-6)} = 9^{3}
\]
Now we need to calculate \( 9^3 \):
\[
9^3 = 9 \times 9 \times 9
\]
Calculating step by step:
\[
9 \times 9 = 81
\]
Now, we multiply that result by 9:
\[
81 \times 9 = 729
\]
Thus, the numerical value of \( 9^9 \times 9^{-6} \) is
\[
\boxed{729}
\]