Here's why:
* Adverbs modify verbs, adjectives, or other adverbs. They answer questions like "how?", "when?", "where?", or "to what extent?".
* "Independently" tells us *how* something is done.
For example:
* "The children worked independently on their projects." (modifies the verb "worked")
* "She is a very independently minded person." (modifies the adjective "minded")