Is this proper notation for a solution?

Your answer is right !!

Method 2 :
x^3 = - 1/27 = [ 1/(3^3) ]*( cosπ + i sin π )
Z k = (1/3)*[ cos (π+2kπ)/3 + i sin (π+2kπ)/3 ]
3 roots as follows:
Z 0 = (1/3)*[ cos π/3 + i sin π/3 ] = (1/3)( 1/2 + i*√3/2 ) = 1/6 + (√3/6) i
Z 1 = (1/3)*[ cos π + i sin π ] = - 1/3
Z 2 = (1/3)*[ cos 5π/3 + i sin 5π/3 ] = (1/3)( 1/2 - i*√3/2 ) = 1/6 - (√3/6) i