You Do Need power plug adapter while traveling from Brunei to Marshall Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Marshall Islands are A and B and in Brunei is G. This is how they look like.

Brunei

In Brunei, outlets of type G are in use.

Type G

Marshall Islands

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

Type A

Type B