A classic hairdo created out of a simple ponytail that can be dressed up is known as a(n):

A classic hairdo created from a simple ponytail and often dressed up is referred to as a chignon. This style typically involves gathering the hair into a low bun at the nape of the neck or slightly higher, which can be secured and finished with various accessories or intricate detailing to enhance its elegance. The key characteristic of a chignon is its versatility; it can be adapted for both casual and formal occasions depending on how it is styled and adorned.

In contrast, while a pleat refers to a folded style that can also be elegant, it does not specifically relate to a ponytail setup. A twist can involve wrapping sections of hair around each other, but it doesn't imply the same bun-like structure that defines a chignon. Blowdrying is a technique for styling hair rather than a specific hairdo. Therefore, a chignon perfectly captures the essence of transforming a simple ponytail into a sophisticated style.