Exponent Calculator

Powers grow astonishingly fast — which is why compound interest, population growth and computer memory all use them. This exponent calculator works out bⁿ for any base and exponent, including negative exponents (reciprocals) and fractional exponents (roots). Whole-number powers of whole numbers are computed exactly, however many digits they have, and a table shows the first few powers so you can see the pattern.

How to use it

Enter the base.
Enter the exponent — whole, negative, decimal or a fraction like 1/2.

Example

A rumour shared with 3 friends, each of whom tells 3 more, reaches 3¹⁰ = 59,049people by the 10th round. Computer memory doubles: 2¹⁰ = 1,024 (a kilobyte), 2²⁰ ≈ 10 lakh (a megabyte). And 27^(1/3) = 3, the cube root of 27. For logarithms — the reverse of powers — use thelog calculator; for money growth, thecompound interest calculator.

Frequently asked questions

What does an exponent mean?

It tells you how many times to multiply the base by itself. 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. A negative exponent means the reciprocal: 2⁻³ = 1/8. A fractional exponent is a root: 8^(1/3) = 2.

What are the laws of exponents?

aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 (for a ≠ 0); a⁻ⁿ = 1/aⁿ.

How big can the answer be?

Whole-number powers are calculated exactly with big-integer arithmetic, so 2^100 shows all 31 digits. Decimal results are shown to 12 significant digits, and very large or small values in scientific notation.

What is 0⁰?

By the usual convention in algebra and combinatorics, 0⁰ = 1, and that is what the calculator shows.