Final answer:
The enzymatic activity encoded by a simple transposon is transposase, which facilitates the movement of the transposon within the genome.
Step-by-step explanation:
The enzymatic activity encoded by a simple transposon is transposase. Transposases catalyze the cut-and-paste as well as the replicative transposition of Class II (DNA) transposons. They enable the transposon to cut from its original location and integrate into another place in the genome. Transposase activity is crucial for the mobilization of Class II transposons. Other enzymes such as reverse transcriptase generate a cDNA copy of retrotransposons, while integrases catalyze insertion of reverse-transcribed retrotransposons, and exonucleases are involved in removing RNA primers. Remember that transposons and the enzymes they encode play significant roles in the mobility and evolutionary impact of genetic elements.