Exponent

An exponent (or power) tells you how many times to multiply the base by itself. In the expression $a^n$, $a$ is the base and $n$ is the exponent.

Core rules:

• $a^m \cdot a^n = a^{m+n}$ (product of powers — add exponents)
• $(a^m)^n = a^{mn}$ (power of a power — multiply)
• $a^{-n} = \frac{1}{a^n}$ (negative exponent — flip the base)
• $a^0 = 1$ for any $a \neq 0$
• $a^{1/n} = \sqrt[n]{a}$ (fractional exponents are roots)

Exponents extend naturally from positive integers to all reals via continuity, and to complex numbers via Euler's formula $e^{i\theta} = \cos\theta + i\sin\theta$. They underlie exponential growth/decay, compound interest, and information theory's logarithm.