# How do you evaluate  (-1)^(2/3)?

Mar 15, 2018

The result is $1$.

#### Explanation:

Use this exponent/radical rule:

${\textcolor{g r e e n}{x}}^{\frac{\textcolor{red}{m}}{\textcolor{b l u e}{n}}} = \sqrt[\textcolor{b l u e}{n}]{{\textcolor{g r e e n}{x}}^{\textcolor{red}{m}}}$

Now here's the expression:

$\textcolor{w h i t e}{=} {\left(\textcolor{g r e e n}{-} \textcolor{g r e e n}{1}\right)}^{\frac{\textcolor{red}{2}}{\textcolor{b l u e}{3}}}$

$= \sqrt[\textcolor{b l u e}{3}]{{\left(\textcolor{g r e e n}{-} \textcolor{g r e e n}{1}\right)}^{\textcolor{red}{2}}}$

$= \sqrt[\textcolor{b l u e}{3}]{1}$

$= 1$

That's the result. Hope this is the answer you were looking for!

Mar 15, 2018

1

#### Explanation:

${x}^{\frac{2}{3}}$ power means the the wholes square of the cubic root of $x$.

Thus, the cubic root of -1 is -1...... and the whole square of the -1 is always +1..