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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

StepWorking
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.

How to Use the Exponent Calculator

  1. Enter the base, the number being multiplied.
  2. Enter the exponent. It can be whole, negative, a decimal or a fraction such as 2/3.
  3. Press Calculate.
  4. Read the result and its scientific notation.
  5. Check the steps table to see how the answer was worked out.

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

Key Terms

  • Base: the number that is multiplied by itself.
  • Exponent or power: how many times the base is used as a factor.
  • Square and cube: a power of 2 and a power of 3.
  • Reciprocal: 1 divided by a number. A negative power gives the reciprocal.
  • Radical: a root, such as a square or cube root, which equals a fraction power.

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

Real-Life Examples

  • Compound growth: $1,000 growing 5% a year for 10 years is 1,000 × 1.05^10 = $1,628.89.
  • Doubling: a population of bacteria that doubles every hour grows by 2^10 = 1,024 times in 10 hours.
  • Computer storage: 2^10 = 1,024 bytes is one kibibyte, and 2^30 bytes is one gibibyte, about 1.07 billion bytes.
  • Roots: the square root of 49 is 49^(1/2) = 7, and the cube root of 125 is 125^(1/3) = 5.
  • Area and volume: a square with 9 ft sides covers 9^2 = 81 sq ft, and a cube with 4 ft sides holds 4^3 = 64 cubic feet.
  • Half-life: after 3 half-lives, (1/2)^3 = 0.125, so 12.5% of a substance remains.

Exponents vs Logarithms

  • Exponent: answers "what is 2 raised to 5?" The answer is 32.
  • Logarithm: answers "2 to what power gives 32?" The answer is 5.
  • The link: if bⁿ = x, then log base b of x = n. They undo each other.
  • Try both: use our Log Calculator to go the other way.

Powers of 2 and 10

n2ⁿ10ⁿ
011
1210
24100
381,000
41610,000
532100,000
8256100,000,000
101,02410,000,000,000
−10.50.1
−20.250.01

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.

Common Mistakes to Avoid

  • Multiplying base and exponent. 3^4 is 81, not 12.
  • Thinking a negative power gives a negative answer. 2^−2 is 0.25.
  • Forgetting brackets with negative bases. (−3)^2 is 9, but −3^2 is usually read as −9.
  • Adding powers of different bases. The product rule only works with the same base: 2^3 × 2^4 = 2^7.
  • Mixing up 0^0. It is undefined or treated as 1 depending on context. This calculator does not allow it.

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.

It is 1,024.

If the bases are the same, add the exponents: 3^2 × 3^4 = 3^6 = 729.

If the bases are the same, subtract the exponents: 5^6 ÷ 5^2 = 5^4 = 625.

Multiply the exponents: (2^3)^2 = 2^6 = 64.

Use scientific notation. For example, 2^50 is about 1.1259 × 10^15. This calculator switches to that form for very big results.

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

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