Evaluate :
(0.027)−23(0.027)^{\dfrac{-2}{3}}(0.027)3−2
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Given,
Simplifying the expression :
⇒(0.027)−23⇒(271000)−23⇒[(310)3]−23⇒(310)3×−23⇒(310)−2⇒(103)2⇒1009.\Rightarrow (0.027)^{\dfrac{-2}{3}} \\[1em] \Rightarrow \Big(\dfrac{27}{1000}\Big)^{-\dfrac{2}{3}} \\[1em] \Rightarrow \Big[\Big(\dfrac{3}{10}\Big)^3\Big]^{-\dfrac{2}{3}} \\[1em] \Rightarrow \Big(\dfrac{3}{10}\Big)^{3 \times -\dfrac{2}{3}} \\[1em] \Rightarrow \Big(\dfrac{3}{10}\Big)^{-2} \\[1em] \Rightarrow \Big(\dfrac{10}{3}\Big)^{2} \\[1em] \Rightarrow \dfrac{100}{9}.⇒(0.027)3−2⇒(100027)−32⇒[(103)3]−32⇒(103)3×−32⇒(103)−2⇒(310)2⇒9100.
Hence, (0.027)−23=1009(0.027)^{\dfrac{-2}{3}} = \dfrac{100}{9}(0.027)3−2=9100.
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(−27)23(-27)^{\dfrac{2}{3}}(−27)32
(0.001)−13(0.001)^{-\dfrac{1}{3}}(0.001)−31
Evaluate the following :
(14)−2−3×(8)23×50+(916)−12\Big(\dfrac{1}{4}\Big)^{-2} - 3 \times (8)^{\dfrac{2}{3}} \times 5^0 + \Big(\dfrac{9}{16}\Big)^{-\dfrac{1}{2}}(41)−2−3×(8)32×50+(169)−21
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