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Exponent Calculator

Raise any number to any power, including negative, decimal and fraction powers such as 1/3, with the steps.

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Steps

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A negative base only gives a real answer with a whole-number power, or a fraction power with an odd bottom number, such as 1/3. Answers are rounded to 10 significant digits.

Quick Answer

An exponent shows how many times to multiply a number by itself. 2^10 means 2 × 2 × … ten times, which is 1,024. A negative power means 1 ÷ the result, so 5^−2 = 1/25 = 0.04. A fraction power is a root: 8^(1/3) is the cube root of 8, which is 2.

Last updated: 2 November 2026 · How we calculate this: exponent and root rules

Table of Contents

How This Exponent Calculator Works

Enter a base and a power. The power can be a whole number, a negative number, a decimal or a fraction such as 2/3. The calculator gives the answer, the scientific notation and the steps.

Quick explanation: bⁿ means b multiplied by itself n times.

  • Negative power: b⁻ⁿ = 1 ÷ bⁿ.
  • Fraction power: b^(p/q) = (q-th root of b)^p.
  • Power of zero: any non-zero number to the power 0 is 1.

Core Formulas

  • Product rule: bᵐ × bⁿ = bᵐ⁺ⁿ
  • Quotient rule: bᵐ ÷ bⁿ = bᵐ⁻ⁿ
  • Power rule: (bᵐ)ⁿ = bᵐⁿ
  • Negative power: b⁻ⁿ = 1 ÷ bⁿ
  • Fraction power: b^(p/q) = (ᵠ√b)^p

Worked Example

Work out 27^(2/3).

  • The bottom number, 3, is the root: cube root of 27 = 3
  • The top number, 2, is the power: 3² = 9
  • So 27^(2/3) = 9

Common Mistakes

  • Negative base: (−2)² = 4, but −2² usually means −(2²) = −4.
  • Negative power: it does not make the answer negative. 2⁻³ = 0.125.
  • Zero: 0 to a negative power is undefined.

Frequently Asked Questions

Multiply the base by itself as many times as the exponent says. For example, 3^4 = 3 × 3 × 3 × 3 = 81.

It means 1 divided by the base to the positive power. So 2^−3 = 1/8 = 0.125.

It is a root. The bottom number is the root and the top number is the power, so 8^(2/3) = 4.

Any non-zero number to the power of 0 is 1.

Not as a real number in most cases. Odd roots such as (−8)^(1/3) = −2 do work.

References & Sources

SourceUsed ForLink
Wikipedia, Exponentiation Exponent rules and definitions. https://en.wikipedia.org/wiki/Exponentiation
Wikipedia, Nth root Roots and fraction powers. https://en.wikipedia.org/wiki/Nth_root