DIY Cost Tools
Exponent Calculator
MATH CALCULATOR
Calculate a base raised to a positive, negative, zero, or decimal exponent.
How it works
An exponent tells how many times a base is used as a factor. Negative exponents produce reciprocals, and fractional exponents represent roots when a real result exists.
Formulas
bⁿ = b × b × … × b (n factors)
b⁻ⁿ = 1 ÷ bⁿ
b⁰ = 1 for b ≠ 0
Example
2¹⁰ = 1,024 because multiplying ten factors of 2 gives 1,024.
Important limits
- Some negative-base fractional powers do not have real-number results.
- Very large or very small answers are limited by browser floating-point precision.
- Zero raised to a negative exponent is undefined.
Frequently asked questions
What does a zero exponent mean?
Any nonzero base raised to the zero power equals 1.
What is a negative exponent?
It indicates the reciprocal of the corresponding positive power.
Checking exponent calculations
An exponent indicates repeated multiplication for positive whole-number powers, but zero, negative, and fractional exponents follow additional rules. For a nonzero base, a zero exponent equals 1. A negative exponent gives the reciprocal, while a fractional exponent represents a root.
Parentheses matter: (-2)² equals 4, but -2² is commonly interpreted as -(2²), which equals -4. Zero raised to a negative power is undefined, and some fractional powers of negative numbers require complex-number results. Large powers can exceed normal calculator ranges, so scientific notation or logarithms may be needed. Keep the full calculated value when it feeds another formula and round only the final answer.
Review notes
The calculator uses standard real-number exponent rules and browser floating-point arithmetic. Last reviewed September 30, 2026.