Final answer:
A neutropenic client should rinse their toothbrush with antibacterial mouthwash or dilute bleach, replace it regularly, and maintain dental health with fluoride toothpaste to prevent infections.
Step-by-step explanation:
The neutropenic client receiving chemotherapy should employ exceptional oral hygiene to reduce the risk of infection due to their compromised immune system. A neutropenic client is advised to rinse their toothbrush with antibacterial mouthwash or a 1:10 dilution of bleach after each use to disinfect it. The toothbrush should also be replaced regularly. While conventional toothpaste containing fluoride can help in maintaining dental health, it is crucial for neutropenic clients to minimize the risk of microbial contamination of their toothbrush as it could lead to severe infections.