Final answer:
The size of the newly constructed pUC19-genex is 4,200 base pairs (bp).
Step-by-step explanation:
The size of the newly constructed pUC19-genex can be determined by adding the size of the pUC19 vector and the size of the insert gene. In this case, the pUC19 vector is commonly known to have a size of approximately 2,700 base pairs (bp). The insert gene is specified to be 1,500 bp long. Therefore, the size of the pUC19-genex construct would be the sum of the two sizes, which is 4,200 bp.