Evaluate:
(22+32)×(12)2(2^2 + 3^2) \times \Big(\dfrac{1}{2}\Big)^2(22+32)×(21)2
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(22+32)×(12)2=(2×2+3×3)×(1×12×2)=(4+9)×(14)=(13)×(14)=(13×14)=(134)=3(14)(2^2 + 3^2) \times \Big(\dfrac{1}{2}\Big)^2\\[1em] = (2 \times 2 + 3 \times 3) \times \Big(\dfrac{1 \times 1}{2 \times 2}\Big)\\[1em] = (4 + 9) \times \Big(\dfrac{1}{4}\Big)\\[1em] = (13) \times \Big(\dfrac{1}{4}\Big)\\[1em] = \Big(\dfrac{13 \times 1}{4}\Big)\\[1em] = \Big(\dfrac{13}{4}\Big)\\[1em] = 3\Big(\dfrac{1}{4}\Big)(22+32)×(21)2=(2×2+3×3)×(2×21×1)=(4+9)×(41)=(13)×(41)=(413×1)=(413)=3(41)
Hence, (22+32)×(12)2=3(14)(2^2 + 3^2) \times \Big(\dfrac{1}{2}\Big)^2 = 3\Big(\dfrac{1}{4}\Big)(22+32)×(21)2=3(41)
Answered By
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[(14)−3−(13)−3]÷(16)−3\Big[\Big(\dfrac{1}{4}\Big)^{-3} - \Big(\dfrac{1}{3}\Big)^{-3}\Big] ÷ \Big(\dfrac{1}{6}\Big)^{-3}[(41)−3−(31)−3]÷(61)−3
