Exponent & Power Calculator (xʸ)
Calculate base raised to any power (xʸ), including negative, fractional, and zero exponents.
Exponent Calculator — interactive calculator, computed instantly in your browser.
Exponent Rules, Radical Roots & Power Algebra (xʸ)
The Core Laws of Exponents and Algebraic Powers
Algebraic Laws: Powers with matching bases combine by adding exponents during multiplication and subtracting exponents during division.
An exponent represents repeated multiplication of a base number by itself: $x^y = x \times x \times \dots \times x$ ($y$ times). In higher mathematics, exponentiation extends to negative numbers, fractional roots, and irrational powers.
1. Fundamental Laws of Exponents Summary
| Law Name | Algebraic Expression | Example |
|---|---|---|
| Zero Exponent Rule | $x^0 = 1 \quad (x \neq 0)$ | $5^0 = 1$ |
| Negative Exponent Rule | $x^{-n} = \frac{1}{x^n}$ | $2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$ |
| Fractional / Radical Rule | $x^{p/q} = \sqrt[q]{x^p}$ | $27^{2/3} = (\sqrt[3]{27})^2 = 3^2 = 9$ |
🔗 Exponents & Power Rules
Exponents represent repeated multiplication and power scaling. Explore our ➗ Math Hub to master polynomial algebra and roots.
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Frequently Asked Questions (Exponent Calculator)
By the quotient rule: x^n / x^n = x^(n - n) = x^0. Since any number divided by itself equals 1, x^0 must equal 1.
In pure algebra, 0⁰ is technically an indeterminate form, though in combinatorics and computer science it is defined as 1 by convention.