Final answer:
The first action a nurse should take when a client's membranes rupture is to observe for a prolapsed cord or meconium-stained fluid, as these conditions are emergent and require immediate attention.
Step-by-step explanation:
When a client comes to the hospital in labor and her membranes rupture, the first action a nurse should take is to observe for a prolapsed cord or meconium-stained fluid. This is crucial because a prolapsed umbilical cord can lead to a critical reduction in blood flow to the fetus, requiring immediate medical intervention. Additionally, the presence of meconium-stained fluid may indicate fetal distress, which also requires prompt attention to prevent complications. After ensuring there are no signs of these emergencies, the nurse should then note the time of the rupture of membranes, as this information is important for monitoring the progression of labor and the potential for infection.