Evaluate:
[{(−15)2}−2]−1\Big[\Big{\Big(-\dfrac{1}{5}\Big)^2\Big}^{-2}\Big]^{-1}[{(−51)2}−2]−1
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[{(−15)2}−2]−1=[{(−1×−15×5)}−2]−1=[{125}−2]−1=[{251}2]−1=[{25×251×1}]−1=[6251]−1=1625\Big[\Big{\Big(-\dfrac{1}{5}\Big)^2\Big}^{-2}\Big]^{-1}\\[1em] = \Big[\Big{\Big(\dfrac{-1 \times -1}{5 \times 5}\Big)\Big}^{-2}\Big]^{-1}\\[1em] = \Big[\Big{\dfrac{1}{25}\Big}^{-2}\Big]^{-1}\\[1em] = \Big[\Big{\dfrac{25}{1}\Big}^2\Big]^{-1}\\[1em] = \Big[\Big{\dfrac{25 \times 25}{1 \times 1}\Big}\Big]^{-1}\\[1em] = \Big[\dfrac{625}{1}\Big]^{-1}\\[1em] = \dfrac{1}{625}[{(−51)2}−2]−1=[{(5×5−1×−1)}−2]−1=[{251}−2]−1=[{125}2]−1=[{1×125×25}]−1=[1625]−1=6251
[{(−15)2}−2]−1=1625\Big[\Big{\Big(-\dfrac{1}{5}\Big)^2\Big}^{-2}\Big]^{-1} = \dfrac{1}{625}[{(−51)2}−2]−1=6251
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