Final answer:
The statement is true; microtubules can grow or shrink independently due to their dynamic nature, allowing them to rapidly assemble and disassemble during processes like cell division.
Step-by-step explanation:
Each microtubule can indeed grow or shrink independently of its neighbors, which is a true statement. Microtubules are dynamic structures composed of polymerized α-tubulin and β-tubulin dimers. These structures are capable of rapid assembly and disassembly, which is facilitated by GTP hydrolysis.
During cell division, for instance, microtubule disassembly assists in the separation and movement of chromatids to opposite poles of the cell, a process known as mitosis or meiosis. This dynamic behavior also allows for the microtubules to quickly reorganize into spindle fibers during cell division, powered by motor proteins such as dynein.