Evaluate the following :
[(27)−39−3]13\Big[\dfrac{(27)^{-3}}{9^{-3}}\Big]^{\dfrac{1}{3}}[9−3(27)−3]31
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Given,
Simplifying the expression :
⇒[(27)−39−3]13⇒[(279)−3]13⇒(279)−3×13⇒(279)−1⇒927⇒13.\Rightarrow \Big[\dfrac{(27)^{-3}}{9^{-3}}\Big]^{\dfrac{1}{3}} \\[1em] \Rightarrow \Big[\Big(\dfrac{27}{9}\Big)^{-3}\Big]^{\dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{27}{9}\Big)^{-3 \times \dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{27}{9}\Big)^{-1} \\[1em] \Rightarrow \dfrac{9}{27} \\[1em] \Rightarrow \dfrac {1}{3}.⇒[9−3(27)−3]31⇒[(927)−3]31⇒(927)−3×31⇒(927)−1⇒279⇒31.
Hence, [(27)−39−3]13=13\Big[\dfrac{(27)^{-3}}{9^{-3}}\Big]^{\dfrac{1}{3}} = \dfrac{1}{3}[9−3(27)−3]31=31.
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