(i) 2700
Resolving 2700 into Prime factor as follows
The Prime factor 2 and 5 do not appear in a groups of three.
Therefore 2700 is not a perfect cube number.
(ii) 16000
Resolving 16000 into Prime factor as follows
Factor 2 is not group of three
∴ 16000 is not a perfect cube.
(iii) 64000
Resolving 64000 into Prime factor as follows
There are perfect cubes of each factor 2, 2, 2 and 5.
∴ 64000 is a perfect cube.
(iv) 900
Resolving 900 into Prime factors as follows
Factors 2, 3 and 5 are not groups of three.
∴ 900 is not a perfect cube.
(v) 125000
Resolving 125000 into Prime factors as follows
Factors 2, 5 and 5 are in groups of three
∴ 125000 is a perfect cube