Evaluate :
33×(243)−23×(9)−133^3 \times (243)^{-\dfrac{2}{3}} \times (9)^{-\dfrac{1}{3}}33×(243)−32×(9)−31
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Simplifying the expression :
⇒33×(35)−23×(32)−13=33×(3)−103×(3)−23=(3)3+(−103)+(−23)=(3)9−10−23=(3)−33=3−1=13.\Rightarrow 3^3 \times (3^5)^{-\dfrac{2}{3}} \times (3^2)^{-\dfrac{1}{3}} \\[1em] = 3^3 \times (3)^{-\dfrac{10}{3}} \times (3)^{-\dfrac{2}{3}} \\[1em] = (3)^{3 + \Big(-\dfrac{10}{3}\Big) + \Big(-\dfrac{2}{3}\Big)} \\[1em] = (3)^{\dfrac{9 - 10 - 2}{3}} = (3)^{\dfrac{-3}{3}} \\[1em] = 3^{-1} = \dfrac{1}{3}.⇒33×(35)−32×(32)−31=33×(3)−310×(3)−32=(3)3+(−310)+(−32)=(3)39−10−2=(3)3−3=3−1=31.
Hence, 33×(243)−23×(9)−13=133^3 \times (243)^{-\dfrac{2}{3}} \times (9)^{-\dfrac{1}{3}} = \dfrac{1}{3}33×(243)−32×(9)−31=31.
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