You Do Need power plug adapter while traveling from Balearic Islands to Cayman Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Cayman Islands are A and B and in Balearic Islands are C and F. This is how they look like.

Balearic Islands

In Balearic Islands, outlets of type C and F are in use.

Type C

Type F

Cayman Islands

In Cayman Islands, outlets of type A and B are in use.

Type A

Type B