**Answer:**

**Bleaching powder:**
Bleaching powder, also known as calcium hypochlorite, is a chemical compound widely used for bleaching, disinfection, and water treatment. It is a white, crystalline solid with a strong chlorine odor.

**Manufacturing process:**
Bleaching powder is manufactured by the action of chlorine gas on dry slaked lime (calcium hydroxide). The chemical reaction involved is as follows:

2Ca(OH)2 + 2Cl2 → Ca(OCl)2 + CaCl2 + 2H2O

**Explanation:**
The correct base used in the manufacture of bleaching powder is calcium hydroxide (option D). Here's why:

1. **Magnesium hydroxide (option A):** Magnesium hydroxide is not used in the manufacture of bleaching powder. It is commonly used as an antacid and laxative. It does not react with chlorine gas to produce bleaching powder.

2. **Sodium hydroxide (option B):** Sodium hydroxide is not used in the manufacture of bleaching powder. It is commonly used in the production of soaps, detergents, and paper. Sodium hydroxide does not react with chlorine gas to produce bleaching powder.

3. **Potassium hydroxide (option C):** Potassium hydroxide is not used in the manufacture of bleaching powder. It is commonly used in the production of potassium salts, soaps, and alkaline batteries. Potassium hydroxide does not react with chlorine gas to produce bleaching powder.

4. **Calcium hydroxide (option D):** Calcium hydroxide is the correct base used in the manufacture of bleaching powder. It reacts with chlorine gas to produce calcium hypochlorite (bleaching powder) along with calcium chloride and water. The chemical reaction is given by:

2Ca(OH)2 + 2Cl2 → Ca(OCl)2 + CaCl2 + 2H2O

Therefore, the correct answer is option D - Calcium hydroxide.