Hawaii’s largest power company warned utility customers across the state on Friday to prepare for power outages that could last for days as a rapidly strengthening tropical storm approaches the islands.

The storm, Lala, is expected to bring heavy rains and winds that could topple trees, especially those with shallow root systems known as the Albizia. The trees can grow as tall as 100 feet, so they can cause significant damage to power lines if they fall.

The utility, Hawaiian Electric, which supplies power on Hawaii Island, Maui and Oahu, also said that customers throughout its service area should avoid any downed power lines. Electrical wires might remain charged when they land on the ground. The utility said that more than 500 workers are ready to restore power.

A much smaller storm last March knocked out power to tens of thousands of customers for as long as a week when a low-pressure system blew across the state, said Jim Kelly, a spokesman for the utility. He said the power company has worked to harden its grid against severe weather and other conditions, but some equipment remains vulnerable to downed trees and windblown debris.

“This is expected to be one of the most dangerous and damaging storms we’ve experienced in a long time,” Mr. Kelly said. He said the storm could bring the most devastation to the state since 2014, when Tropical Storm Iselle caused widespread damage that required months of recovery.

The Hawaii Emergency Management Agency urged residents to prepare for heavy rain and flash flooding by clearing gutters and drains, and by raising valuable possessions off the ground. The agency also recommended covering windows and glass doors; sealing gaps in doors and trim to prevent wind and rain from entering; securing outdoor objects like patio furniture and plants that could be blown by strong winds; and removing dead, damaged or overhanging tree limbs that may threaten property.

The Island of Hawaii, known as the Big Island, could experience some of the most severe conditions as the eye of the storm crosses its southern tip late Saturday. The roads on the rural areas of the island can make it difficult for crews to respond to damaged utility equipment, Mr. Kelly said. That, coupled with the inability to immediately receive support from crews in other states, could hamper efforts to quickly restore service.

But because the island has endured volcanic eruptions, earthquakes and hurricanes, Mr. Kelly believes residents know how to contend with difficult conditions.

“They’ve had it all,” Mr. Kelly said.