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Mathematics

Evaluate:

14+(0.01)12×(5)(27)23\sqrt\dfrac{1}{4} + (0.01)^{-\dfrac{1}{2}} \times (5) - (27)^\dfrac{2}{3}

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Answer

14+(0.01)12×5(27)23=12+(10.01)12×5(33)23=12+(1001)12×5(3)2×33=12+100×5(3)2=12+10×59=12+509=12+41=1+822=832=4112\sqrt\dfrac{1}{4} + (0.01)^{-\dfrac{1}{2}} \times 5 - (27)^\dfrac{2}{3}\\[1em] = \dfrac{1}{2} + \Big(\dfrac{1}{0.01}\Big)^{\dfrac{1}{2}} \times 5 - (3^3)^\dfrac{2}{3}\\[1em] = \dfrac{1}{2} + \Big(\dfrac{100}{1}\Big)^{\dfrac{1}{2}} \times 5 - (3)^\dfrac{2 \times 3}{3}\\[1em] = \dfrac{1}{2} + \sqrt{100} \times 5 - (3)^2\\[1em] = \dfrac{1}{2} + 10 \times 5 - 9\\[1em] = \dfrac{1}{2} + 50 - 9\\[1em] = \dfrac{1}{2} + 41\\[1em] = \dfrac{1 + 82}{2}\\[1em] = \dfrac{83}{2}\\[1em] = 41\dfrac{1}{2}

Hence, 14+(0.01)12×(5)(27)23=4112\sqrt\dfrac{1}{4} + (0.01)^{-\dfrac{1}{2}} \times (5) - (27)^\dfrac{2}{3} = 41\dfrac{1}{2}.

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