Why do you use exponents?

Exponents are used in many different contexts and for different, though related, reasons.

Exponents are used in scientific notation to represent very large and very small numbers. The main purpose it to strip the number of unnecessary detail and to reduce the risk of errors.

Exponents are used in algebra and calculus to deal with exponential or power functions. Many laws in physics, for example, involve powers (positive, negative or fractional) of basic measures. Calculations based on these laws are simper if exponents are used.