The minimum number of cycles necessary to replicate a fragment of DNA over 500 times is 9 cycles. In Polymerase Chain Reaction (PCR) method, the fragments of DNA are doubled in each cycle. This means that after "n" cycles, the total number of fragments is given by the equation 2^n. In this case, after 9 cycles a total of 512 DNA fragments will be obtained, because 2^9 is equal to 512.
