What is five thirds to the negative third?

Answer 1

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:

• Cube_root(1/5)*(1/2 + i*sqrt(3)/2)
• Cube_root(1/5)*(1/2 - i*sqrt(3)/2)

Where i represents the square root of -1. (Imaginary unit).

Answer 2

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.

Answer 3

1/125