Simplify the following:
(32)25×(4)−12×(8)132−2÷(64)−13\dfrac{(32)^{\dfrac{2}{5}} \times (4)^{-\dfrac{1}{2}} \times (8)^{\dfrac{1}{3}}}{2^{-2} ÷ (64)^{-\dfrac{1}{3}}}2−2÷(64)−31(32)52×(4)−21×(8)31
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Given,
⇒(32)25×(4)−12×(8)132−2÷(64)−13⇒(25)25×(22)−12×(23)132−2÷(26)−13⇒22×2−1×212−2÷2−2⇒22−1+12−22−2⇒221=22=4.\Rightarrow \dfrac{(32)^{\dfrac{2}{5}} \times (4)^{-\dfrac{1}{2}} \times (8)^{\dfrac{1}{3}}}{2^{-2} ÷ (64)^{-\dfrac{1}{3}}} \\[1em] \Rightarrow \dfrac{(2^5)^{\dfrac{2}{5}} \times (2^2)^{-\dfrac{1}{2}} \times (2^3)^{\dfrac{1}{3}}}{2^{-2} ÷ (2^6)^{-\dfrac{1}{3}}} \\[1em] \Rightarrow \dfrac{2^2 \times 2^{-1} \times 2^1}{2^{-2} ÷ 2^{-2}} \\[1em] \Rightarrow \dfrac{2^{2 - 1 + 1}}{\dfrac{2^{-2}}{2^{-2}}} \\[1em] \Rightarrow \dfrac{2^2}{1} = 2^2 = 4.⇒2−2÷(64)−31(32)52×(4)−21×(8)31⇒2−2÷(26)−31(25)52×(22)−21×(23)31⇒2−2÷2−222×2−1×21⇒2−22−222−1+1⇒122=22=4.
Hence, (32)25×(4)−12×(8)132−2÷(64)−13\dfrac{(32)^{\dfrac{2}{5}} \times (4)^{-\dfrac{1}{2}} \times (8)^{\dfrac{1}{3}}}{2^{-2} ÷ (64)^{-\dfrac{1}{3}}}2−2÷(64)−31(32)52×(4)−21×(8)31 = 4.
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