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Mathematics

Evaluate:

(27)2\Big(\dfrac{2}{7}\Big)^{-2}

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Answer

(27)2=(72)2=(7×72×2)=494=1214\Big(\dfrac{2}{7}\Big)^{-2}\\[1em] = \Big(\dfrac{7}{2}\Big)^2\\[1em] = \Big(\dfrac{7 \times 7}{2 \times 2}\Big)\\[1em] = \dfrac{49}{4}\\[1em] = 12\dfrac{1}{4}

Hence, (27)2=1214\Big(\dfrac{2}{7}\Big)^{-2} = 12\dfrac{1}{4}.

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