Polymerase chain reaction (PCR) is a process to amplify nucleic acid sequences. In this process, the DNA is replicated multiples times by adding synthesized primer which attach to the denatured DNA strand and are extended using a thermostable polymerase enzyme -Taq polymerase obtained from a thermophilic bacterium, Thermus aquaticus. DNA is denatured by heating and breaking the H-bonds.

In each cycle of PCR the dsDNA is doubled, so after n cycles the copies of DNA will be $2^{\mathrm{n}}$ .

Now the given sample of viral DNA is single stranded, therefore, in the first cycle it will form a dsDNA. And in the consecutive cycles the dsDNA will double in copies. Therefore, after 10 cycles the number of copies will be $2^9=512$ .