Evaluate the following :
14+(0.01)−12−(27)23×30\sqrt{\dfrac{1}{4}} + (0.01)^{\dfrac{-1}{2}} - (27)^{\dfrac{2}{3}} \times 3^041+(0.01)2−1−(27)32×30
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Given,
Simplifying the expression :
⇒14+(0.01)−12−(27)23×30⇒12+(1100)−12−[(3)3]23×1⇒12+(100)12−(3)2⇒12+[(10)2]12−9⇒12+10−9⇒12+1⇒1+22⇒32⇒112.\Rightarrow \sqrt{\dfrac{1}{4}} + (0.01)^{\dfrac{-1}{2}} - (27)^{\dfrac{2}{3}} \times 3^0 \\[1em] \Rightarrow \dfrac{1}{2} + \Big(\dfrac{1}{100}\Big)^{\dfrac{-1}{2}} - [(3)^3]^{\dfrac{2}{3}} \times 1 \\[1em] \Rightarrow \dfrac{1}{2} + (100)^{\dfrac{1}{2}} - (3)^2 \\[1em] \Rightarrow \dfrac{1}{2} + [(10)^2]^{\dfrac{1}{2}} - 9 \\[1em] \Rightarrow \dfrac{1}{2} + 10 - 9 \\[1em] \Rightarrow \dfrac{1}{2} + 1 \\[1em] \Rightarrow \dfrac{1 + 2}{2} \\[1em] \Rightarrow \dfrac{3}{2} \\[1em] \Rightarrow 1\dfrac{1}{2}.⇒41+(0.01)2−1−(27)32×30⇒21+(1001)2−1−[(3)3]32×1⇒21+(100)21−(3)2⇒21+[(10)2]21−9⇒21+10−9⇒21+1⇒21+2⇒23⇒121.
Hence, 14+(0.01)−12−(27)23×30=112\sqrt{\dfrac{1}{4}} + (0.01)^{\dfrac{-1}{2}} - (27)^{\dfrac{2}{3}} \times 3^0 = 1\dfrac{1}{2}41+(0.01)2−1−(27)32×30=121.
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