Question

the value of 1/3^-2​

Answer 1

Step-by-step explanation:

(-1)^2/3 = 1^1/3.

Every number has 3 cube roots. Let's find the cube roots of 1. It's equivalent to finding the roots of this cubic :

x^3-1 = 0.

(x-1)(x^2 + x + 1) = 0.

x - 1 = 0 or x^2 + x + 1 = 0.

x = 1.

To find other 2 roots, we've to solve this quadratic.

A quadratic formula yields :

x = (-1 ± √(3)i)/2.