(8−43÷2−2)\Big(8^{-\dfrac{4}{3}} ÷ 2^{-2}\Big)(8−34÷2−2) is equal to :
14\dfrac{1}{4}41
−14-\dfrac{1}{4}−41
−12-\dfrac{1}{2}−21
12\dfrac{1}{2}21
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Simplifying the expression :
⇒(8−43÷2−2)=[(23)−43÷122]=[2−4÷122]=124÷122=124×22=122=14.\Rightarrow \Big(8^{-\dfrac{4}{3}} ÷ 2^{-2}\Big) = \Big[(2^3)^{-\dfrac{4}{3}} ÷ \dfrac{1}{2^2}\Big] \\[1em] = \Big[2^{-4} ÷ \dfrac{1}{2^2}\Big] \\[1em] = \dfrac{1}{2^4} ÷ \dfrac{1}{2^2} \\[1em] = \dfrac{1}{2^4} \times 2^2 \\[1em] = \dfrac{1}{2^2} \\[1em] = \dfrac{1}{4}.⇒(8−34÷2−2)=[(23)−34÷221]=[2−4÷221]=241÷221=241×22=221=41.
Hence, Option 1 is the correct option.
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