The fundamental and derived quantities are related through mathematical equations or expressions. Derived quantities are obtained from fundamental quantities by performing mathematical operations, such as multiplication, division, addition, or subtraction. Here's how the fundamental and derived quantities are related:

1. Multiplication or Division: Some derived quantities are obtained by multiplying or dividing fundamental quantities. For example:

- Speed = Distance/Time

- Density = Mass/Volume

2. Exponents and Roots: Derived quantities can involve fundamental quantities raised to certain powers or roots. For example:

- Area = Length^2

- Volume = Length^3

3. Combination of Operations: Many derived quantities involve a combination of mathematical operations. For instance:

- Acceleration = (Final Velocity - Initial Velocity)/Time

- Force = Mass * Acceleration

4. Constants and Conversion Factors: Certain derived quantities involve constants or conversion factors that relate different units. For example:

- 1 Newton (N) = 1 kg * m/s^2

- 1 Joule (J) = 1 N * m

5. Physical Laws and Equations: Many derived quantities are defined based on fundamental principles or physical laws. For example:

- Gravitational Force = (Gravitational Constant * Mass 1 * Mass 2) / Distance^2

In summary, the fundamental quantities serve as building blocks upon which derived quantities are constructed through mathematical operations, combinations of fundamental quantities, and physical principles. Derived quantities are expressed in terms of fundamental quantities and allow us to describe and measure various physical phenomena and properties in the real world.