Exponent Calculator
Quickly calculate the result of a number raised to any power. This tool handles both positive and negative exponents, as well as fractional powers.
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Understanding Exponents and Powers
An exponent is a mathematical notation that indicates how many times a number, called the base, is multiplied by itself. It's a powerful way to express very large or very small numbers concisely. This Exponent Calculator allows you to easily compute the result of raising a base to any given power.
The Basics of Exponents
In the expression bⁿ:
- b is the base: the number being multiplied.
- n is the exponent (or power): the number of times the base is multiplied by itself.
For example, 5³ means 5 × 5 × 5, which equals 125.
Rules of Exponents
Exponents follow several key rules that are essential for algebra and other areas of mathematics. This calculator handles these rules automatically.
| Rule Name | Formula | Example |
|---|---|---|
| Product Rule | xᵐ × xⁿ = xᵐ⁺ⁿ | 2² × 2³ = 2⁵ = 32 |
| Quotient Rule | xᵐ / xⁿ = xᵐ⁻ⁿ | 3⁵ / 3² = 3³ = 27 |
| Power Rule | (xᵐ)ⁿ = xᵐⁿ | (4²)³ = 4⁶ = 4096 |
| Zero Exponent | x⁰ = 1 | 10⁰ = 1 |
| Negative Exponent | x⁻ⁿ = 1 / xⁿ | 5⁻² = 1 / 5² = 1/25 |
| Fractional Exponent | x¹/ⁿ = ⁿ√x | 9¹/² = √9 = 3 |
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