How do you simplify $(-27)^(-2/3)$ ?

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Answer 1 · 2017-03-12T20:00:35

$1/9$

Since $a^(m/n)=root(n)(a^m)$

and

$a^-m=1/(a^m)$

then

$(-27)^(-2/3)=(-1/27)^(2/3)=root(3)((-1/27)^2)$

Since $27=3^3$ , you get

$root(3)((-1/3)^6)=(-1/3)^2=1/9$

Answer 2 · 2017-03-12T21:39:01

$1/9$

Consider the example $x^(-2/3)$ this is the same as $1/x^(2/3)$

Using this as our guide:

Write $(-27)^(-2/3)$ as $1/(-27)^(2/3)$

This is the same as $1/root(3)((-27)^2)$

But I have just spotted something!
Lets take advantage of the fact that $(-3)xx(-3)xx(-3)=-27$

So changing the order we do things, write as:

$1/(root(3)(-27))^2 = 1/((-3)^2) = 1/9$

How do you simplify (-27)^(-2/3)(-27)^(-2/3)?