Step 1: Understanding the Concept
In each PCR cycle (denaturation, annealing and extension) the amount of DNA doubles.
Step 2: Calculation
Starting with one DNA segment, the number of copies after \(n\) cycles is \(2^{n}\).
For 9 cycles: \(2^{9} = 512\).
Step 3: Compare the options
512 is the fourth option.
Final Answer:
512 copies are produced after 9 cycles.
\[ \boxed{\text{(D) }512} \]