How do you evaluate ${(- 1)}^{\frac{2}{3}}$ $(-1)^(2/3)$ ?

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Answer 1 · 2018-03-15T03:41:29

The result is $1$ $1$ .

Use this exponent/radical rule:

$x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ $color(green)x^(color(red)m/color(blue)n)=rootcolor(blue)n(color(green)x^color(red)m)$

Now here's the expression:

$= {(- 1)}^{\frac{2}{3}}$ $color(white)=(color(green)-color(green)1)^(color(red)2/color(blue)3)$

$= \sqrt[3]{{(- 1)}^{2}}$ $=rootcolor(blue)3((color(green)-color(green)1)^color(red)2)$

$= \sqrt[3]{1}$ $=rootcolor(blue)3 1$

$= 1$ $=1$

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

Answer 2 · 2018-03-15T03:42:29

1

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

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

How do you evaluate (-1)^(2/3)(−1)23 (-1)^(2/3)?