Evaluate :
(8125)−13\Big(\dfrac{8}{125}\Big)^{-\dfrac{1}{3}}(1258)−31
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Given,
Simplifying the expression :
⇒(8125)−13⇒[(25)3]−13⇒(25)3×−13⇒(25)−1⇒52.\Rightarrow \Big(\dfrac{8}{125}\Big)^{-\dfrac{1}{3}} \\[1em] \Rightarrow \Big[\Big(\dfrac{2}{5}\Big)^3\Big]^{-\dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{2}{5}\Big)^{3 \times -\dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{2}{5}\Big)^{-1} \\[1em] \Rightarrow \dfrac{5}{2}.⇒(1258)−31⇒[(52)3]−31⇒(52)3×−31⇒(52)−1⇒25.
Hence, (8125)−13=52\Big(\dfrac{8}{125}\Big)^{-\dfrac{1}{3}} = \dfrac{5}{2}(1258)−31=25.
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