(9^-3/9^-7)^-2
You asked:
Evaluate the expression: \({\left( \frac{{9}^{-3}}{{9}^{-7}} \right)}^{-2}\)
MathBot Answer:
\[{\left( \frac{{9}^{-3}}{{9}^{-7}} \right)}^{-2} = \frac{1}{43046721} \approx 0.00000002323057312541877463791028\]
\[\begin{aligned}{\left( \frac{{9}^{-3}}{{9}^{-7}} \right)}^{-2}& = \frac{1}{\left(\frac{1}{9^{3}} \cdot \frac{1}{\frac{1}{9^{7}}}\right)^{2}}\\& = \frac{1}{\left(\frac{1}{729} \cdot \frac{1}{\frac{1}{9^{7}}}\right)^{2}}\\& = \frac{1}{\left(\frac{1}{729} \cdot \frac{1}{\frac{1}{4782969}}\right)^{2}}\\& = \frac{1}{6561^{2}}\\& = \frac{1}{43046721}\end{aligned}\]