Exponent / Power Calculator

Raise a base to a positive, negative, fractional, or zero exponent.

Enter your values

Change any field. The result is recalculated on this device.

Formula, example and assumptions
Power1,024

Your result

Local calculation
Power1,024

The result raises the base to the entered exponent. Negative exponents produce reciprocals, while fractional exponents can represent roots within the supported real-number range.

Base
2
Exponent
10
See how this is calculated
Check the inputs and method

These are your current inputs, not the worked example further down the page.

Base
2
Exponent
10

Method

For positive integer n, aⁿ is a multiplied by itself n times. a⁻ⁿ = 1/aⁿ for a ≠ 0. For positive a, aᵇ = exp(b × ln a).

Read the worked example and assumptions

How this calculation works

A power raises a base to an exponent. Whole positive exponents represent repeated multiplication, negative exponents take reciprocals, and fractional exponents can represent roots. The calculator evaluates a finite real-number result; it does not return complex roots for unsupported inputs.

For positive integer n, aⁿ is a multiplied by itself n times. a⁻ⁿ = 1/aⁿ for a ≠ 0. For positive a, aᵇ = exp(b × ln a).

Worked example

This example uses illustrative inputs. Your current result is shown above.

With base 2 and exponent 10, 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024.

Assumptions and limits

  • Zero raised to a negative exponent has no finite result.
  • Negative bases with fractional exponents are limited by real-number numeric evaluation; the tool does not perform symbolic rational-root simplification.
  • Very large or tiny nonzero results outside the supported numeric range produce an error. The numeric convention returns 1 for 0⁰; some mathematical contexts leave it undefined.

Questions people ask

What does a negative exponent mean?

It changes multiplication into a reciprocal, not a negative answer. For example, a positive base raised to −2 means one divided by its square.

Why can a negative base give an error?

Many fractional powers of negative values are not real. Even an intended rational exponent can be entered only as a rounded decimal, so use a symbolic method when the exact fraction matters.

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