(i) \((4^{-1}\times 3^{-1})^{2}\)

⇒ \((\frac{1}{4}\times \frac{1}{3})^{2}\)[Using \(a^{-n}=\frac{1}{a^{n}}\);\(a^{2}=a\times a\)] 

⇒ \(\frac{1}{12}\times \frac{1}{12}\) = \(\frac{1}{144}\)

(ii) \((5^{-1}\div 6^{-1})^{3}\)

⇒ \((\frac{1}{5}\times \frac{1}{6})^{3}\)[Using \(a^{-n}=\frac{1}{a^{n}}\);\(a^{n}=a\times a..........n\,times\)]

⇒  \((\frac{1}{5}\times \frac{6}{1})^{3}\) = \((\frac{6}{5})^{3}\)=\(\frac{216}{125}\)[Using and \(\frac{1}{a}\div \frac{1}{b}\)=\(\frac{1}{a}\times \frac{b}{1}\)] 

(iii) \((2^{-1}\div 4^{-1})\div 2^{-2}\)

⇒   \((\frac{1}{2}\times \frac{1}{4})\)\(\div \frac{1}{2^{2}}\)[Using \(a^{-n}=\frac{1}{a^{n}}\);\(a^{2}=a\times a\)]

⇒ \(\frac{1}{8}\times \frac{4}{1}\) = \(\frac{1}{2}\)[Using and \(\frac{1}{a}\div \frac{1}{b}\)=\(\frac{1}{a}\times \frac{b}{1}\)] 

(iv) \((3^{-1}\times 4^{-1})\times 5^{-1}\)

⇒ \((\frac{1}{3}\times \frac{1}{4})\times \frac{1}{5}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)] 

⇒   \(\frac{1}{12}\times \frac{1}{5}\) = \(\frac{1}{60}\)