Simplify the following:
22×2564643−(12)−2\dfrac{\sqrt{2^2} \times \sqrt[4]{256}}{\sqrt[3]{64}} - \Big(\dfrac{1}{2}\Big)^{-2}36422×4256−(21)−2
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Given,
⇒22×2564643−(12)−2⇒22×284263−(2)2⇒(22)12×(28)14(26)13−4⇒(2)2×12×(2)8×14(2)6×13−4⇒2×2222−4⇒2−4⇒−2.\Rightarrow \dfrac{\sqrt{2^2} \times \sqrt[4]{256}}{\sqrt[3]{64}} - \Big(\dfrac{1}{2}\Big)^{-2} \\[1em] \Rightarrow \dfrac{\sqrt{2^2} \times \sqrt[4]{2^8}}{\sqrt[3]{2^6}} - (2)^{2} \\[1em] \Rightarrow \dfrac{(2^2)^{\dfrac{1}{2}} \times (2^8)^{\dfrac{1}{4}}}{(2^6)^{\dfrac{1}{3}}} - 4 \\[1em] \Rightarrow \dfrac{(2)^{2 \times \dfrac{1}{2}} \times (2)^{8 \times \dfrac{1}{4}}}{(2)^{6 \times \dfrac{1}{3}}} - 4 \\[1em] \Rightarrow \dfrac{2 \times 2^2}{2^2} - 4 \\[1em] \Rightarrow 2 - 4 \\[1em] \Rightarrow -2.⇒36422×4256−(21)−2⇒32622×428−(2)2⇒(26)31(22)21×(28)41−4⇒(2)6×31(2)2×21×(2)8×41−4⇒222×22−4⇒2−4⇒−2.
Hence, 22×2564643−(12)−2\dfrac{\sqrt{2^2} \times \sqrt[4]{256}}{\sqrt[3]{64}} - \Big(\dfrac{1}{2}\Big)^{-2}36422×4256−(21)−2 = -2.
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