Exponent Calculator
Calculate base raised to a power.
Exponential Expression
Expression:
23
Result
Result
8
Expanded Form
2^3 = 2 × 2 × 2 = 8
Properties:
Base: 2
Exponent: 3
About This Calculator
The Exponent Calculator helps you compute exponential expressions of the form base^exponent. It supports positive and negative integers, fractional exponents, and handles very large or very small results with scientific notation.
This calculator can compute any base raised to any power, including negative exponents (which represent reciprocals) and fractional exponents (which represent roots). It's useful for mathematical calculations, scientific computations, and educational purposes.
Formula & Calculation Method
Exponent Rules:
Basic: aⁿ = a × a × ... × a (n times)
Zero Exponent: a⁰ = 1 (a ≠ 0)
Negative Exponent: a⁻ⁿ = 1 / aⁿ
Fractional Exponent: a^(m/n) = ⁿ√(aᵐ)
Product Rule: aᵐ × aⁿ = a^(m+n)
Quotient Rule: aᵐ / aⁿ = a^(m-n)
Power Rule: (aᵐ)ⁿ = a^(m×n)
Exponents represent repeated multiplication. A positive exponent means multiply the base by itself that many times. A negative exponent means take the reciprocal. A fractional exponent represents a root (e.g., a^(1/2) = √a).
How to Use This Calculator
- Enter Base: Input the base number (the number being raised to a power).
- Enter Exponent: Input the exponent (the power to raise the base to).
- View Results: See the calculated result, expanded form, and scientific notation if applicable.
- Special Cases: Any number to the power of 0 equals 1. Negative exponents represent reciprocals.
Frequently Asked Questions
What happens when the exponent is 0?
Any non-zero number raised to the power of 0 equals 1. This is a fundamental rule of exponents: a⁰ = 1 for any a ≠ 0. 0⁰ is undefined.
How do negative exponents work?
A negative exponent represents the reciprocal of the base raised to the positive exponent. For example, 2⁻³ = 1 / 2³ = 1/8 = 0.125. The negative sign "flips" the fraction.
What are fractional exponents?
Fractional exponents represent roots. For example, a^(1/2) = √a (square root), a^(1/3) = ∛a (cube root), and a^(m/n) = ⁿ√(aᵐ) (nth root of a to the mth power).
Can I use decimal exponents?
Yes, decimal exponents are supported. For example, 2^1.5 = 2^(3/2) = √(2³) = √8 ≈ 2.828. The calculator handles any real number as an exponent.
Expert Reviewed
This calculator was reviewed by NumCalculators Editorial Team, Multi-disciplinary Expert Team