An exponent indicates how many times a number (the base) is multiplied by itself.
In aⁿ, "a" is the base and "n" is the exponent. For example, 2³ = 2 × 2 × 2 = 8. Exponents can be positive integers, zero, negative numbers, fractions (roots), or decimals. Key laws include aᵐ × aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, and a⁻ⁿ = 1/aⁿ. Exponents are fundamental in scientific notation, exponential growth/decay, compound interest, and all higher mathematics.
The concept of exponents dates back to Archimedes who described large numbers using powers of 10. The modern exponent notation was introduced by René Descartes in his 1637 work "La Géométrie." Negative and fractional exponents were developed by John Wallis and Isaac Newton in the 17th century. Leonhard Euler later connected exponents with logarithms and complex numbers.