North Carolina is about 275 times bigger than Palau.

Palau is approximately 459 sq km, while North Carolina is approximately 126,161 sq km, making North Carolina 27,386% larger than Palau. Meanwhile, the population of Palau is ~21,695 people (9.5 million more people live in North Carolina).
Tip: This to-scale comparison of Palau vs. North Carolina uses the Mercator projection, which distorts the size of regions near the poles.