(i) \(\{4^{-1}\times 3^{-1}\}^{2}\)

⇒ \((\frac{1}{4}\times \frac{1}{3})^{2}\)= \((\frac{1}{12})^{2}\)= \(\frac{1}{144}\)[Using \(a^{-n}\)=\(\frac{1}{a^{n}}\); \(a^{n}\)=\(a\times a...... .......n\, times\)] 

(ii) \(\{5^{-1}\div 6^{-1}\}^{3}\)

⇒ \((\frac{1}{5}\div \frac{1}{6})^{3}\)[Using  \(a^{-n}\)=\(\frac{1}{a^{n}}\) ] 

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

⇒ \(\frac{6^3}{5^3}\)=\(\frac{216}{125}\)[Using  \(a^{n}\)=\(a\times a...... .......n\, times\)] 

(iii) \((2^{-1}+3^{-1})^{-1}\)

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

⇒ \((\frac{3+2}{6})^{-1}\)= \((\frac{5}{6})^{-1}\)= \(\frac{6}{5}\)[Using \(a^{-n}\)=\(\frac{1}{a^{n}}\)] 

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

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

⇒ \((\frac{1}{12})^{-1}\times \frac{1}{5}\)= \(\frac{12}{5}\)[Using \(a^{-n}\)=\(\frac{1}{a^{n}}\)] 

(v) \((4^{-1}-5^{-1})^{-1}\div 3^{-1}\)

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

⇒ \((\frac{5-4}{20})^{-1}\times 3\)[Using and \(\frac{1}{a}\div \frac{1}{b}\)= \(\frac{1}{a}\times \frac{1}{b}\) ]

⇒ \(\frac{1}{20}\times 3\)= \(\frac{3}{20}\)