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

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Answer 1 · 2018-03-15T03:41:29

The result is #1#.

Use this exponent/radical rule:

#color(green)x^(color(red)m/color(blue)n)=rootcolor(blue)n(color(green)x^color(red)m)#

Now here's the expression:

#color(white)=(color(green)-color(green)1)^(color(red)2/color(blue)3)#

#=rootcolor(blue)3((color(green)-color(green)1)^color(red)2)#

#=rootcolor(blue)3 1#

#=1#

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

Answer 2 · 2018-03-15T03:42:29

1

#x^(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..