1. \(\displaystyle{\left(-{27}\right)}^{{-\frac{{2}}{{3}}}}=\frac{{1}}{{\left(-{27}\right)}^{{\frac{{2}}{{3}}}}}\)

2. \(1 /( - 27 ) ^ {( 2 / 3 )} = 1 /( ( - 27 ^ {( 1 / 3)} ) ^2= 1 / ( \sqrt{- 27 })^ 2 = 1 / ( -3 )^2 = 1 / 9\)

3. another answer

\(\displaystyle{\left(-{27}\right)}^{{-\frac{{2}}{{3}}}}={\left({\left(-{27}\right)}^{{\frac{{1}}{{3}}}}\right)}^{{-{{2}}}}\) \(=(\sqrt{ - 27 } )^{ -2} = ( - 3 )^ {-2} = 1 / (- 3 )^2 = 1 / 9\)

\(\displaystyle{\left({X}\right)}^{-}{m}=\frac{{1}}{{\left({X}\right)}^{{m}}}\)

\(\displaystyle{\left({X}\right)}^{{\frac{{m}}{{n}}}}={\left({X}^{{\frac{{1}}{{n}}}}\right)}^{{m}}\)

\(\displaystyle{X}^{{\frac{{1}}{{3}}}}\) = \(\sqrt X. \sqrt{- 27}= -3\)

\(\displaystyle{X}^{{\frac{{1}}{{3}}}}\) = \(\sqrt X. \sqrt{- 27}= -3\)

\(\displaystyle{\left({X}\right)}^{-}{m}=\frac{{1}}{{\left({X}\right)}^{{m}}}\)