Evaluate:
[−37]−5×[73]2\Big[-\dfrac{3}{7}\Big]^{-5} \times \Big[\dfrac{7}{3}\Big]^2[−73]−5×[37]2
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[−37]−5×[73]2=[−73]5×[73]2=[−7535]×[7232]=[−75+235+2]=[−7737]\Big[-\dfrac{3}{7}\Big]^{-5} \times \Big[\dfrac{7}{3}\Big]^2\\[1em] = \Big[-\dfrac{7}{3}\Big]^5 \times \Big[\dfrac{7}{3}\Big]^2\\[1em] = \Big[-\dfrac{7^5}{3^5}\Big] \times \Big[\dfrac{7^2}{3^2}\Big]\\[1em] = \Big[-\dfrac{7^{5+2}}{3^{5+2}}\Big]\\[1em] = \Big[-\dfrac{7^{7}}{3^{7}}\Big][−73]−5×[37]2=[−37]5×[37]2=[−3575]×[3272]=[−35+275+2]=[−3777]
Hence,[−37]−5×[73]2=[−7737]\Big[-\dfrac{3}{7}\Big]^{-5} \times \Big[\dfrac{7}{3}\Big]^2 = \Big[-\dfrac{7^{7}}{3^{7}}\Big][−73]−5×[37]2=[−3777].
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