Find the solution for m such that:

Let's raise the exponent three on both sides of the equation.

1/x^2 = (x^m) ^3

1/x^2 = x^ (3m)

1 = x^2. x^ (3m)

1 = x^ (2+3m)

X^ (2+3m) = 1

For this to be true:

2+3m = 0

3m = - 2

m = - 2/3