Question

(-27)^-2/3

Equation, expression, and inequalitie
ANSWERED
asked 2020-11-03
\(\displaystyle\frac{{\left(-{27}\right)}^{{-{{2}}}}}{{3}}\)

Answers (1)

2020-11-04

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

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