Exponent Calculator
Calculate powers, exponents, and scientific notation instantly. Get step-by-step mathematical breakdowns for your algebra and calculus problems.
Calculate Your Powers
Enter your base number and exponent to receive a detailed, step-by-step mathematical breakdown of the result, including scientific notation for extreme values.
Exponent Parameters
Define your mathematical expression (xⁿ)
Solution Evaluation
Step-by-step mathematical breakdown
Laws of Exponents
Fundamental algebraic rules used to simplify and solve exponential expressions.
| Rule Name | Formula | Example |
|---|---|---|
| Product Rule | xᵃ × xᵇ = xᵃ⁺ᵇ | 2³ × 2² = 2⁵ = 32 |
| Quotient Rule | xᵃ / xᵇ = xᵃ⁻ᵇ | 5⁴ / 5² = 5² = 25 |
| Power Rule | (xᵃ)ᵇ = xᵃᵇ | (3²)³ = 3⁶ = 729 |
| Zero Exponent | x⁰ = 1 | 7⁰ = 1 |
| Negative Exponent | x⁻ᵃ = 1 / xᵃ | 2⁻³ = 1 / 2³ = 0.125 |
| Fractional Exponent | x^(1/n) = ⁿ√x | 9^(1/2) = √9 = 3 |
Exponent Math FAQ
Everything you need to know about calculating powers and exponential expressions.
An exponent (or power) indicates how many times a number, known as the base, is multiplied by itself. For example, in 2³, 2 is the base and 3 is the exponent, meaning 2 × 2 × 2 = 8.
Any non-zero number raised to the power of zero is exactly 1. This is a fundamental rule of exponents derived from the quotient rule (xⁿ / xⁿ = x⁰ = 1). The expression 0⁰ is mathematically indeterminate, though often defined as 1 in computing contexts.
A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example, x⁻ⁿ = 1 / (xⁿ). So, 2⁻³ = 1 / (2³) = 1/8 = 0.125.
Yes. A fractional exponent represents a root. For example, x^(1/2) is the square root of x, and x^(1/3) is the cube root of x. Decimal exponents are simply fractional exponents in decimal form (e.g., x^0.5 is the same as x^(1/2)).