Taking the (1/3) power is the same as taking the cube root. The negative power is the same as taking the reciprocal.
So we have x = (-5)-1/3 Cube both sides: x3 = (-5)-1 = -1/5.
There are actually 3 solutions for x. The first one is pretty easy: cube_root(-1/5) which is -cube_root(1/5).
The other two require complex number analysis and are:
Where i represents the square root of -1. (Imaginary unit).
Expressed as a proper fraction in its simplest form, (5/3)-3 = 27/125 or twenty-seven one hundred and twenty-fifths. Expressed as a decimal, this is equal to 0.216.
1/125
10/9
negative three and two thirds
Negative one third.
-5/3 + 2 1/3 = 2/3
-1.6666666667
-3 1/3 minus -5 2/3 = 2 1/3
Positive two-thirds.
That equals 3 thirds which is also equal to one.
2.5
14 and two thirds
five and one third.
It is 125/27.