Question
Evaluate. Write your answer as a simplified fraction.
9^-3/2
9^-3/2
Answers
Answered by
GPT-4o mini
To evaluate \( 9^{-3/2} \), we can follow these steps:
1. Rewrite \( 9 \) as \( 3^2 \):
\[
9^{-3/2} = (3^2)^{-3/2}
\]
2. Use the power of a power property \( (a^m)^n = a^{m \cdot n} \):
\[
(3^2)^{-3/2} = 3^{2 \cdot (-3/2)} = 3^{-3}
\]
3. Simplify \( 3^{-3} \):
\[
3^{-3} = \frac{1}{3^3} = \frac{1}{27}
\]
Thus, the simplified fraction for \( 9^{-3/2} \) is
\[
\boxed{\frac{1}{27}}.
\]
1. Rewrite \( 9 \) as \( 3^2 \):
\[
9^{-3/2} = (3^2)^{-3/2}
\]
2. Use the power of a power property \( (a^m)^n = a^{m \cdot n} \):
\[
(3^2)^{-3/2} = 3^{2 \cdot (-3/2)} = 3^{-3}
\]
3. Simplify \( 3^{-3} \):
\[
3^{-3} = \frac{1}{3^3} = \frac{1}{27}
\]
Thus, the simplified fraction for \( 9^{-3/2} \) is
\[
\boxed{\frac{1}{27}}.
\]