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Answer :
(i)We have:\([(\frac{1}3)^{-1}-(\frac{1}4)^{-1}]^{-1}\)
\(=(3^1-4^1)^{-1}=(-1)^{-1}=\frac{1}{(-1)^1}=\frac{1}{-1}=-1\)
(ii)We have: \((\frac{5}8)^{-7}\times (\frac{8}5)^{-4}\)
\(=(\frac{8}5)^7\times(\frac{5}8)^4=\frac{8^7}{5^7}\times\frac{5^4}{8^4}\)
\(=\frac{8^{7-4}}{5^{7-4}}=\frac{8^3}{5^3}=\frac{512}{125}\)