6.Evaluate:
(i)\([(\frac{1}3)^{-1}-(\frac{1}4)^{-1}]^{-1}\)

(ii)\((\frac{5}8)^{-7}\times (\frac{8}5)^{-4}\)

(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: \((\frac{5}8)^{-7}\times (\frac{8}5)^{-4}\)
\(=(\frac{8}5)^7\times(\frac{5}8)^4=\frac{8^7}{5^7}\times\frac{5^4}{8^4}\)

\(=\frac{8^{7-4}}{5^{7-4}}=\frac{8^3}{5^3}=\frac{512}{125}\)