What sign should a nurse observe for a lack of fat-soluble vitamins in a client with a T-tube bile drainage?

The observation of easy bruising is indicative of a potential deficiency in fat-soluble vitamins, particularly vitamin K. This vitamin is crucial for the synthesis of certain proteins that are required for blood coagulation. When a patient has a T-tube for bile drainage, the absorption of fat-soluble vitamins (A, D, E, and K) can be compromised.

In this situation, the loss of bile affects the digestion and absorption of dietary fats and fat-soluble vitamins. A lack of vitamin K can lead to a decrease in clotting factors, resulting in easy bruising. This symptom serves as a clear sign that the patient may be lacking in these essential nutrients due to their current condition.

Other choices like weight gain, dry skin, and increased appetite do not directly correlate with the deficiencies caused by impaired fat absorption. Thus, easy bruising stands out as the most relevant sign related to fat-soluble vitamin deficiency in this context.