Final answer:
Transposase is the enzyme encoded by a simple transposon, facilitating its movement within the genome.
Step-by-step explanation:
The enzymatic activity encoded by a simple transposon is transposase. Transposase is the enzyme responsible for facilitating the cut-and-paste or replicative transposition of Class II (DNA) transposons. This enzyme allows the transposon to move from one location to another within the genome. In contrast to transposase, other enzymes like reverse transcriptase and integrase are specifically associated with retrotransposons (Class I transposons), which utilize an RNA intermediate during the transposition process. These retrotransposons require a promoter that recognizes a reverse transcriptase enzyme, along with endonuclease and integrase enzymes.