This exponent calculator computes any power: base raised to an exponent, including negative exponents (which give fractions) and fractional exponents (which give roots). Enter the base and exponent to get the result with the rule behind it.
What Is an Exponent?
An exponent tells you how many times to multiply a number (the base) by itself: 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Exponents are the engine of growth — compound interest, population growth, radioactive decay and computer memory (all those powers of 2) are exponents at work. This calculator is part of our Math Calculators collection; its inverse operation is the Logarithm Calculator.
Exponent Examples (Verified)
- 2¹⁰ = 1,024 — ten doublings; why a kilobyte is 1,024 bytes.
- 10⁻² = 0.01 — negative exponents flip to reciprocals: 10⁻² = 1/100.
- 9^0.5 = 3 — a fractional exponent of ½ is a square root.
- 5⁰ = 1 — every non-zero base to the power zero is 1.
The Exponent Rules
- Multiply same bases: xᵃ × xᵇ = xᵃ⁺ᵇ
- Divide same bases: xᵃ ÷ xᵇ = xᵃ⁻ᵇ
- Power of a power: (xᵃ)ᵇ = xᵃᵇ
- Negative exponent: x⁻ⁿ = 1 ÷ xⁿ
- Fractional exponent: x^(1/n) = the n-th root of x; x^(m/n) = (n-th root of x)^m
- Zero exponent: x⁰ = 1 (for x ≠ 0)
Roots deserve their own tool when you need them simplified — see the Square Root Calculator, which shows forms like 5√2.
Powers of 2 Worth Memorizing
| Power | Value | Where it appears |
|---|---|---|
| 2⁸ | 256 | Bytes and pixel values |
| 2¹⁰ | 1,024 | Kilobytes, chess doublings |
| 2¹⁶ | 65,536 | Old spreadsheet rows, ports |
| 2²⁰ | 1,048,576 | Megabytes |
| 2³² | ≈ 4.29 billion | IPv4 addresses, 32-bit limits |
Related Tools
- Logarithm Calculator — the inverse operation
- Square Root Calculator — exponent ½, specialized
- Scientific Notation Calculator — powers of 10 formatting
Frequently Asked Questions
How do I calculate an exponent?
Multiply the base by itself exponent times: 3⁴ = 3 × 3 × 3 × 3 = 81. For negative or fractional exponents, use the rules above — or this calculator.
What does a negative exponent mean?
A reciprocal: x⁻ⁿ = 1/xⁿ. So 2⁻³ = 1/8 = 0.125. It does not make the result negative.
Why is anything to the power 0 equal to 1?
From the division rule: xⁿ ÷ xⁿ = x⁰, and anything divided by itself is 1.
What is 0⁰?
Undefined (indeterminate) in general mathematics — this calculator reports it as undefined too.
How are exponents used in finance?
Compound growth: future value = principal × (1 + rate)^years — exponents are why time in the market matters so much.
Is this exponent calculator free?
Yes — free, instant, no sign-up.