Question
is 9^-9 . 9^-8= to one ninth^17
Answers
GPT-4o mini
To simplify the expression \( 9^{-9} \cdot 9^{-8} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
Applying this to the expression:
\[
9^{-9} \cdot 9^{-8} = 9^{-9 + (-8)} = 9^{-17}
\]
Now we want to see if this is equal to \( \frac{1}{9^{17}} \), which can also be written as \( 9^{-17} \):
\[
\frac{1}{9^{17}} = 9^{-17}
\]
So, indeed, we have:
\[
9^{-9} \cdot 9^{-8} = 9^{-17} = \frac{1}{9^{17}}
\]
Thus, the statement \( 9^{-9} \cdot 9^{-8} = \frac{1}{9^{17}} \) is true.
Applying this to the expression:
\[
9^{-9} \cdot 9^{-8} = 9^{-9 + (-8)} = 9^{-17}
\]
Now we want to see if this is equal to \( \frac{1}{9^{17}} \), which can also be written as \( 9^{-17} \):
\[
\frac{1}{9^{17}} = 9^{-17}
\]
So, indeed, we have:
\[
9^{-9} \cdot 9^{-8} = 9^{-17} = \frac{1}{9^{17}}
\]
Thus, the statement \( 9^{-9} \cdot 9^{-8} = \frac{1}{9^{17}} \) is true.