Evaluate:
[−25]4×[−52]2\Big[-\dfrac{2}{5}\Big]^4 \times \Big[-\dfrac{5}{2}\Big]^2[−52]4×[−25]2
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[−25]4×[−52]2=[−2454]×[−5222]=[−2454]×[−2−25−2]=[24−254−2]=[2252]=[425]\Big[-\dfrac{2}{5}\Big]^4 \times \Big[-\dfrac{5}{2}\Big]^2\\[1em] = \Big[\dfrac{-2^4}{5^4}\Big] \times \Big[\dfrac{-5^2}{2^2}\Big]\\[1em] = \Big[\dfrac{-2^4}{5^4}\Big] \times \Big[\dfrac{-2^{-2}}{5^{-2}}\Big]\\[1em] = \Big[\dfrac{2^{4-2}}{5^{4-2}}\Big]\\[1em] = \Big[\dfrac{2^2}{5^2}\Big]\\[1em] = \Big[\dfrac{4}{25}\Big][−52]4×[−25]2=[54−24]×[22−52]=[54−24]×[5−2−2−2]=[54−224−2]=[5222]=[254]
Hence,[−25]4×[−52]2=[425]\Big[-\dfrac{2}{5}\Big]^4 \times \Big[-\dfrac{5}{2}\Big]^2 = \Big[\dfrac{4}{25}\Big][−52]4×[−25]2=[254].
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