Compute:
(125)−23÷(8)23(125)^{-\dfrac{2}{3}} ÷ (8)^{\dfrac{2}{3}}(125)−32÷(8)32
1 Like
(125)−23÷(8)23=(53)−23÷(23)23=(5)−3×23÷(2)3×23=(5)−2÷(2)2=(5)−2×(12)2=(5)−2×14=(15)2×14=125×14=1100(125)^{-\dfrac{2}{3}} ÷ (8)^{\dfrac{2}{3}}\\[1em] = (5^3)^{-\dfrac{2}{3}} ÷ (2^3)^{\dfrac{2}{3}}\\[1em] = (5)^{-3\times\dfrac{2}{3}} ÷ (2)^{3\times\dfrac{2}{3}}\\[1em] = (5)^{-2} ÷ (2)^{2}\\[1em] = (5)^{-2} \times \Big(\dfrac{1}{2}\Big)^{2}\\[1em] = (5)^{-2} \times \dfrac{1}{4}\\[1em] = \Big(\dfrac{1}{5}\Big)^2 \times \dfrac{1}{4}\\[1em] = \dfrac{1}{25} \times \dfrac{1}{4}\\[1em] = \dfrac{1}{100}(125)−32÷(8)32=(53)−32÷(23)32=(5)−3×32÷(2)3×32=(5)−2÷(2)2=(5)−2×(21)2=(5)−2×41=(51)2×41=251×41=1001
(125)−23÷(8)23=1100(125)^{-\dfrac{2}{3}} ÷ (8)^{\dfrac{2}{3}} = \dfrac{1}{100}(125)−32÷(8)32=1001
Answered By
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