Simplify the following:
(−127)−23\Big(-\dfrac{1}{27}\Big)^{-\dfrac{2}{3}}(−271)−32
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Given,
⇒(−127)−23=(−27)23=(−3)3×23=(−3)2=9.\Rightarrow \Big(-\dfrac{1}{27}\Big)^{-\dfrac{2}{3}} = (-27)^{\dfrac{2}{3}} \\[1em] = (-3)^{3 \times \dfrac{2}{3}} = (-3)^2 \\[1em] = 9.⇒(−271)−32=(−27)32=(−3)3×32=(−3)2=9.
Hence, (−127)−23\Big(-\dfrac{1}{27}\Big)^{-\dfrac{2}{3}}(−271)−32 = 9.
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