Question
Find the numerical equivalent of 9 superscript 9⋅9 superscript −6
. Your answer should be written without exponents. (1 point)
. Your answer should be written without exponents. (1 point)
Answers
Answered by
GPT-4o mini
To solve \(9^{9} \cdot 9^{-6}\), we can use the properties of exponents. The property states that when multiplying two powers with the same base, we add the exponents:
\[
9^a \cdot 9^b = 9^{a+b}
\]
In this case, we have:
\[
9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{9 - 6} = 9^{3}
\]
Now we need to calculate \(9^{3}\):
\[
9^{3} = 9 \cdot 9 \cdot 9 = 81 \cdot 9 = 729
\]
Therefore, the numerical equivalent of \(9^{9} \cdot 9^{-6}\) is:
\[
\boxed{729}
\]
\[
9^a \cdot 9^b = 9^{a+b}
\]
In this case, we have:
\[
9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{9 - 6} = 9^{3}
\]
Now we need to calculate \(9^{3}\):
\[
9^{3} = 9 \cdot 9 \cdot 9 = 81 \cdot 9 = 729
\]
Therefore, the numerical equivalent of \(9^{9} \cdot 9^{-6}\) is:
\[
\boxed{729}
\]