The smallest unit of power is the watt (W). Let's understand why the watt is considered the smallest unit of power.

The definition of power is the rate at which work is done or energy is transferred. It is the measure of how quickly or slowly a certain amount of work is done or energy is used. In other words, power tells us how fast or slow something is happening.

The watt is named after James Watt, an 18th-century Scottish engineer who made significant contributions to the development of the steam engine. He is known for inventing the horsepower unit of power, but the watt is a smaller unit and is widely used in the International System of Units (SI).

Power can be calculated by dividing the amount of work done by the time it takes to do that work. Mathematically, power (P) is equal to work (W) divided by time (t). Therefore, the unit of power is derived from the units of work and time.

Here's why the other options are not the smallest unit of power:

b) Kilowatt (kW): A kilowatt is equal to 1000 watts. It is a larger unit of power commonly used in electrical systems or to measure the power output of engines or appliances.

c) Horsepower (hp): Horsepower is a unit of power that was originally derived by James Watt to compare the power output of steam engines to that of horses. One horsepower is equal to approximately 745.7 watts. While it is widely used in the automotive and engineering industries, it is not the smallest unit of power.

d) Milliwatt (mW): A milliwatt is equal to one thousandth (1/1000) of a watt. It is a smaller unit of power commonly used in electronics, telecommunications, and other low-power applications. However, the watt is still smaller than the milliwatt and is considered the smallest unit of power.

In conclusion, the watt is the smallest unit of power as it is the base unit in the SI system. It is derived from the fundamental units of work and time, making it the most commonly used unit for measuring power.