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

2 Answers | Add Yours

Top Answer

embizze's profile pic

Posted on

(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`

oldnick's profile pic

Posted on

`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`

We’ve answered 327,688 questions. We can answer yours, too.

Ask a question