You Do Need power plug adapter while traveling from Bhutan to Pitcairn Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Pitcairn Islands is I and in Bhutan are C, D and G. This is how they look like.

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I