[(11/9)^-9*(9/11)^-4]/[(9/11)^0]

asked by guest
on Nov 10, 2024 at 1:39 am



You asked:

Evaluate the expression: \(\frac{{\left( \frac{11}{9} \right)}^{-9} \cdot {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}}\)

MathBot Answer:

\[\frac{{\left( \frac{11}{9} \right)}^{-9} \cdot {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}} = \frac{59049}{161051} \approx 0.36664783205320053895970841534669\]

\[\begin{aligned}\frac{{\left( \frac{11}{9} \right)}^{-9} \cdot {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}}& = \frac{1}{\left(\frac{11}{9}\right)^{9}} \cdot \frac{1}{\left(\frac{9}{11}\right)^{4}} \cdot \frac{1}{\left(\frac{9}{11}\right)^{0}}\\& = \frac{387420489}{2357947691} \cdot \frac{1}{\left(\frac{9}{11}\right)^{4}} \cdot \frac{1}{\left(\frac{9}{11}\right)^{0}}\\& = \frac{387420489}{2357947691} \cdot \frac{14641}{6561} \cdot \frac{1}{\left(\frac{9}{11}\right)^{0}}\\& = \frac{387420489}{2357947691} \cdot \frac{14641}{6561} \cdot 1^{-1}\\& = \frac{387420489}{2357947691} \cdot \frac{14641}{6561}\\& = \frac{59049}{161051}\end{aligned}\]

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