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Please help me solve/compute this question!

 

Please compute:

(-8)^{-2/3}

 

It would be helpful to answer it ASAP. Thanks!

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 Sep 9, 2018
 #1
avatar+7350 
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\(\phantom{=\,}(-8)^{-\frac23}\\ \)

 

\( =\,\frac{1}{(-8)^{\frac23}}\)          because      \(x^{-a}\,=\,\frac{1}{x^a}\)

 

\( =\,\frac{1}{(-8)^{\frac23}}\cdot\frac{(-8)^\frac13}{(-8)^\frac13}\)

 

\( =\,\frac{(-8)^{\frac13}}{(-8)^{\frac23+\frac13}}\)          because     \(x^a\cdot x^b\,=\,x^{a+b}\)

 

\( =\,\frac{(-8)^{\frac13}}{(-8)^{\frac33}}\)

 

\( =\,\frac{(-8)^{\frac13}}{(-8)^{1}}\)

 

\( =\,\frac{-2}{-8}\)

 

\( =\,\frac14\)

.
 Sep 9, 2018

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