Final answer:
An enhancer is the correct term for a regulatory sequence of DNA that can increase gene expression when mutated, even from a distance of 10,000 base pairs away.
Step-by-step explanation:
The regulatory sequence of DNA that is 10,000 base pairs away from the gene it regulates and causes an increase in expression when mutated would best be called an enhancer. Enhancers are binding sequences that are part of the intricate regulation of gene expression. They consist of short DNA sequences called distal control elements. When activator proteins bind to these elements, they interact with mediator proteins and transcription factors, bending the DNA to facilitate the necessary interactions. These interactions result in an increase in gene transcription when the enhancer is functioning properly. Therefore, a mutation in an enhancer sequence that leads to increased gene expression indicates that this regulatory element is amplifying the gene's activity.