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How do I simplify these? 1. (-216)^(-2/3) 2. -(-27)^(-4/3)

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samanthahuber | Student, Undergraduate | eNoter

Posted May 12, 2013 at 1:42 AM via web

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How do I simplify these?

1. (-216)^(-2/3)

2. -(-27)^(-4/3)

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Top Answer

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 12, 2013 at 1:58 AM (Answer #1)

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(1) Simplify `(-216)^(-2/3)`

Rewrite as `1/(-216)^(2/3)` using `a^(-b)=1/a^b`

Rewrite as `1/((-216)^(1/3))^2` using `a^(mn)=(a^m)^n`

The cubed root of -216 is -6:

`=1/(-6)^2`

`=1/36`

(2) Simplify `-(-27)^(-4/3)`

`=(-1)/((-27)^(4/3))`

`=(-1)/((-27)^(1/3))^4`

`=(-1)/(-3)^4`

`=-1/81`

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oldnick | Valedictorian

Posted May 12, 2013 at 2:22 AM (Answer #2)

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`216^(-2/3)=1/root(3)(216^2)` `=1/root(3)((6^3)^2)` `=1/root(3)((6^2)^3)=` `1/6^2=1/36`

`-(-27)^(-4^3)=(-1)(-1 xx 27)^(-4/3)` `=(-1)(-1)^(-4/3) xx 27^(-4/3)=`

`=(-1) xx 1/root(3)((-1)^4)xx 1/root(3)((3^3)^4)` `=(-1) xx 1/root(3)(1) xx 1/root(3)((3^4)^3)=`

`=-1 xx 1/3^4=-1/81`

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