Evaluate :
(0.001)−13(0.001)^{-\dfrac{1}{3}}(0.001)−31
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Given,
Simplifying the expression :
⇒(0.001)−13⇒(11000)−13⇒[(110)3]−13⇒(110)3×−13⇒(110)−1⇒10.\Rightarrow (0.001)^{-\dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{1}{1000}\Big)^{-\dfrac{1}{3}} \\[1em] \Rightarrow \Big[\Big(\dfrac{1}{10}\Big)^3\Big]^{-\dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{1}{10}\Big)^{3 \times -\dfrac{1}{3}} \\[1em] \Rightarrow \Big(\dfrac{1}{10}\Big)^{-1} \\[1em] \Rightarrow 10.⇒(0.001)−31⇒(10001)−31⇒[(101)3]−31⇒(101)3×−31⇒(101)−1⇒10.
Hence, (0.001)−13=10(0.001)^{-\dfrac{1}{3}} = 10(0.001)−31=10.
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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
