Final answer:
The nurse should cleanse the affected area with mild soap and water to maintain cleanliness, prevent infection, and promote healing. Cold compresses, prophylactic antibiotics, and muscle relaxants are not recommended in this situation without further indication.
Step-by-step explanation:
A nurse in an emergency department caring for a toddler with partial-thickness burns on their right arm should cleanse the affected area with mild soap and water. This first aid step is crucial in maintaining clean burn wounds, preventing infection, and promoting healing. Cleansing with mild soap and water is generally recommended rather than applying cold compresses, which can exacerbate tissue damage, or initiating prophylactic antibiotic use without a clear indication of infection or a physician's order. Muscle relaxants are not typically administered for partial-thickness burns unless there is another indication for their use.