Final answer:
In a client with hyperthyroidism after a subtotal thyroidectomy, the nurse should monitor the serum levels of thyroid hormones, specifically T3 and T4, as they indicate the effectiveness of the surgery and the client's thyroid function.
Step-by-step explanation:
In a client with hyperthyroidism who has undergone a subtotal thyroidectomy, the nurse should closely monitor the client's serum laboratory values. One serum laboratory value that requires intervention by the nurse is the level of thyroid hormone, specifically triiodothyronine (T3) and thyroxine (T4). These thyroid hormones regulate the metabolic rate and can indicate the effectiveness of the surgery and the client's thyroid function.