Exponent Calculator
Calculate exponents and powers ($x^n$). Supports negative bases, negative exponents, and decimals. Shows step-by-step expansion for integer powers.
How Exponents Work
An exponent refers to the number of times a number (the base) is multiplied by itself. It is written as a small number to the upper right of the base number: xⁿ.
- x (Base): The number to be multiplied.
- n (Exponent): The number of times to multiply the base.
Examples
- 2³ = 2 × 2 × 2 = 8
- 5² = 5 × 5 = 25
- 10¹ = 10
Negative Exponents
A negative exponent means you divide 1 by the base raised to the positive exponent. It represents the reciprocal.
x⁻ⁿ = 1 / xⁿ
Example: 2⁻³ = 1 / 2³ = 1 / 8 = 0.125
Zero Exponent
Any non-zero number raised to the power of 0 is always 1.
Example: 5⁰ = 1, 123⁰ = 1.
? Frequently Asked Questions
This is a mathematical ambiguity. In many contexts (algebra, combinatorics), it is defined as 1. In analysis (calculus), it is often treated as an indeterminate form.
Yes. A decimal (fractional) exponent represents a root. For example, x^0.5 is the same as the square root of x (√x).
If the result is very large or very small, it may be displayed in Scientific Notation. For example, 1.5e+12 means 1.5 × 10^12.