[(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: (119)−9(911)−4(911)0\frac{{\left( \frac{11}{9} \right)}^{-9} {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}}

MathBot Answer:

(119)−9(911)−4(911)0=59049161051≈0.36664783205320053895970841534669\frac{{\left( \frac{11}{9} \right)}^{-9} {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}} = \frac{59049}{161051} \approx 0.36664783205320053895970841534669

(119)−9(911)−4(911)0=3874204892357947691(911)−4(911)0=3874204892357947691⋅146416561(911)0=59049161051(911)0=590491610511=59049161051\begin{aligned}\frac{{\left( \frac{11}{9} \right)}^{-9} {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}}&=\frac{\frac{387420489}{2357947691} {\left( \frac{9}{11} \right)}^{-4}}{{\left( \frac{9}{11} \right)}^{0}}\\&=\frac{\frac{387420489}{2357947691} \cdot \frac{14641}{6561}}{{\left( \frac{9}{11} \right)}^{0}}\\&=\frac{\frac{59049}{161051}}{{\left( \frac{9}{11} \right)}^{0}}\\&=\frac{\frac{59049}{161051}}{1}\\&=\frac{59049}{161051}\end{aligned}

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