Exponentiation Calculator: Calculate Powers Easily

Understanding Exponentiation

**Exponentiation** is a mathematical operation involving a **base** b and an **exponent** n. It is written as bⁿ and pronounced as "b raised to the power of n".

When n is a positive integer, exponentiation corresponds to repeated multiplication of the base:

b^n = b * b * ... * b (n times)

For example, 2³ = 2 × 2 × 2 = 8. In this expression, 2 is the base, 3 is the exponent, and 8 is the power.

Special Cases & Rules

Zero Exponent: Any non-zero base raised to 0 is always 1 (e.g. b⁰ = 1). 0⁰ is mathematically undefined.
Negative Exponents: Represents the reciprocal of the base raised to the positive power: b^-n = 1 / bⁿ.
Fractional Exponents: Represents radicals. For example, b^1/2 = √b and b^p/q = ^q√b^p.
Negative Base & Fractional Exponent: Can result in complex numbers (e.g., (-4)^0.5 = √-4 = 2i).