Exponent Calculator
Calculate any power (base^exponent) instantly. Supports positive, negative, and fractional exponents with step-by-step explanations.
Enter Base and Exponent
Common Powers of 2
Understanding Exponents
An exponent (also called power or index) tells you how many times to multiply a number by itself. For example, 2³ = 2 × 2 × 2 = 8.
Exponent Rules
- x⁰ = 1 — Any number to the power of 0 equals 1
- x¹ = x — Any number to the power of 1 equals itself
- x⁻ⁿ = 1/xⁿ — Negative exponents become reciprocals
- xᵃ × xᵇ = xᵃ⁺ᵇ — Add exponents when multiplying same base
- xᵃ ÷ xᵇ = xᵃ⁻ᵇ — Subtract exponents when dividing same base
- (xᵃ)ᵇ = xᵃˣᵇ — Multiply exponents when raising to a power
- xᵃ/ᵇ = ᵇ√(xᵃ) — Fractional exponents become roots
Real-World Applications
- Computer Science: Binary (powers of 2), data storage
- Finance: Compound interest calculations
- Science: Scientific notation (10ⁿ)
- Population Growth: Exponential models
- Physics: Inverse square laws
Frequently Asked Questions
In mathematics, 0⁰ is considered "indeterminate" because different contexts give different answers. Our calculator returns 1, which is the most common convention in combinatorics.
A fractional exponent like x^(1/2) equals the square root of x. Similarly, x^(1/3) is the cube root. The numerator becomes the power, the denominator becomes the root.
Scientific notation uses powers of 10 to express very large or small numbers. For example, 3.5 million = 3.5 × 10⁶, and 0.000001 = 1 × 10⁻⁶.
Because computers use binary (base 2), powers of 2 are fundamental. 2¹⁰ = 1024 ≈ 1000, which is why we have "kilobytes" (1024 bytes) and similar units.