(3^9/3^5)^-2
You asked:
Evaluate the expression: \({\left( \frac{{3}^{9}}{{3}^{5}} \right)}^{-2}\)
MathBot Answer:
\[{\left( \frac{{3}^{9}}{{3}^{5}} \right)}^{-2} = \frac{1}{6561} \approx 0.00015241579027587258039932937052\]
\[\begin{aligned}{\left( \frac{{3}^{9}}{{3}^{5}} \right)}^{-2}& = \frac{1}{\left(3^{9} \cdot \frac{1}{3^{5}}\right)^{2}}\\& = \frac{1}{\left(19683 \cdot \frac{1}{3^{5}}\right)^{2}}\\& = \frac{1}{\left(\frac{19683}{243}\right)^{2}}\\& = \frac{1}{81^{2}}\\& = \frac{1}{6561}\end{aligned}\]