Exponent Calculator
Calculate basepower — any real base, any real exponent
Enter Values
Base
base
^
Exponent (Power)
exp
— = —
Powers Reference Table
| Expression | Result |
|---|
Result
—
Scientific: —
log₁₀(result)—
ⁿ√(result) = base—
Exponent Rules
- Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ
- Quotient rule: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- Power of a power: (aᵐ)ⁿ = aᵐⁿ
- Negative exponent: a⁻ⁿ = 1/aⁿ
- Zero exponent: a⁰ = 1 (for any a ≠ 0)
- Fractional exponent: a^(1/n) = ⁿ√a (nth root)
lightbulb Common Powers
12¹⁰ = 1,024 ≈ 1 KB (memory units)
22²⁰ = 1,048,576 ≈ 1 MB
310⁹ = 1 billion (crore × 100)
✓ e^1 = 2.71828... (Euler's number)
quizFrequently Asked Questions
What is the difference between an exponent and a power?
They're often used interchangeably. In 2⁵, the base is 2, the exponent is 5, and the result (32) is the power. The notation means "multiply 2 by itself 5 times." Technically, "power" refers to the result; "exponent" refers to the superscript number that tells you how many times to multiply.
What are negative exponents?
A negative exponent means the reciprocal: 2⁻³ = 1/2³ = 1/8 = 0.125. This appears in scientific notation for very small numbers — for example, 10⁻⁶ = 0.000001 (one millionth). The rule is: aⁿ × a⁻ⁿ = 1.
What is 0 raised to the power of 0?
0⁰ is mathematically indeterminate — different branches of mathematics treat it differently. In combinatorics and most calculators, 0⁰ is defined as 1 for convenience (it simplifies many formulas). In calculus, it is treated as an indeterminate form. This calculator follows the common convention that 0⁰ = 1.