Evaluate :
(27125)23×(925)−32\Big(\dfrac{27}{125}\Big)^{\dfrac{2}{3}} \times \Big(\dfrac{9}{25}\Big)^{-\dfrac{3}{2}}(12527)32×(259)−23
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Simplifying the expression :
⇒(27125)23×(925)−32=[(35)3]23×[(35)2]−32=(35)2×(35)−3=(35)2+(−3)=(35)−1=53=123.\Rightarrow \Big(\dfrac{27}{125}\Big)^{\dfrac{2}{3}} \times \Big(\dfrac{9}{25}\Big)^{-\dfrac{3}{2}} = \Big[\Big(\dfrac{3}{5}\Big)^3\Big]^{\dfrac{2}{3}} \times \Big[\Big(\dfrac{3}{5}\Big)^2\Big]^{-\dfrac{3}{2}} \\[1em] = \Big(\dfrac{3}{5}\Big)^2 \times \Big(\dfrac{3}{5}\Big)^{-3} = \Big(\dfrac{3}{5}\Big)^{2 + (-3)} \\[1em] = \Big(\dfrac{3}{5}\Big)^{-1} = \dfrac{5}{3} = 1\dfrac{2}{3}.⇒(12527)32×(259)−23=[(53)3]32×[(53)2]−23=(53)2×(53)−3=(53)2+(−3)=(53)−1=35=132.
Hence, (27125)23×(925)−32=123\Big(\dfrac{27}{125}\Big)^{\dfrac{2}{3}} \times \Big(\dfrac{9}{25}\Big)^{-\dfrac{3}{2}} = 1\dfrac{2}{3}(12527)32×(259)−23=132.
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