(i) 392 is a perfect cube.

False.

Prime factors of 392 = 2 × 2 × 2 × 7 × 7 = 2³ × 7²

(ii) 8640 is not a perfect cube.

True

Prime factors of 8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2³ × 2³ × 3³ × 5

(iii) No cube can end with exactly two zeros.

True

Beause a perfect cube always have zeros in multiple of 3.

(iv) There is no perfect cube which ends in 4.

False

64 is a perfect cube = 4 × 4 × 4 and it ends with 4.

(v) For an integer a, a³ is always greater than a².

False

In case of negative integers ,

=

(vi) If a and b are integers such that a²>b², then a³>b³.

False

In case of negative integers,

=

But ,

(vii) If a divides b, then a³ divides b³.

True

If a divides b =

=

For each value of b and a its true.

(viii) If a² ends in 9, then a³ ends in 7.

False

Let a = 7

7² = 49 and 7³ = 343

(ix) If a² ends in an even number of zeros, then a³ ends in 25.

False

Let a = 20

= a² = 20² = 400 and a³ = 8000

(x) If a² ends in an even number of zeros, then a³ ends in an odd number of zeros.

False

Let a = 100

= a² = 100² = 10000 and a³ = 100³ = 1000000