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  4. Exponent Calculator

Exponent Calculator

Solve base^exponent = result for any missing value — with optional base e and exponent laws.

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How it works

Exponentiation relates a base, an exponent, and a result. Fill in any two fields to solve for the third. Real-valued results only.

base^exponent = result

When to use

Use this tool when you need to: leave the unknown blank. Check “Use e as base” for natural exponential growth (eˣ).

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Leave the unknown blank. Check “Use e as base” for natural exponential growth (eˣ).

Frequently asked questions

What is the Exponent Calculator?
Exponentiation relates a base, an exponent, and a result. Fill in any two fields to solve for the third. Real-valued results only.
How do I use the Exponent Calculator?
Enter the required values, then calculate. The Exponent Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Exponent Calculator use?
base^exponent = result

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Exponentiation

Enter any two of base, exponent, and result to solve for the third. Real numbers only — imaginary results are not computed.

^
=

Leave the unknown blank. Use decimals for fractional powers (0.5 = square root).

Try an example

How it works

What is an exponent?

Exponentiation is written aⁿ with base a and exponent n. When n is a positive integer, it means multiplying the base by itself n times: aⁿ = a × a × … × a (n times) This calculator accepts negative bases but does not compute imaginary numbers. Enter fractional exponents in decimal form (for example 0.5).

Basic exponent laws

Same base, multiply → add exponents: aⁿ × aᵐ = aⁿ⁺ᵐ Negative exponent → reciprocal: a⁻ⁿ = 1 / aⁿ Same base, divide → subtract: aᵐ / aⁿ = aᵐ⁻ⁿ Power of a power → multiply: (aᵐ)ⁿ = aᵐⁿ Distribute over products and quotients: (ab)ⁿ = aⁿbⁿ and (a/b)ⁿ = aⁿ/bⁿ Special cases: a¹ = a, and a⁰ = 1 (including the common convention 0⁰ = 1 for many applications).

Negative bases and fractional exponents

A negative base raised to an integer exponent follows the usual sign rules (even → positive, odd → negative). Fractional exponents of a negative base often require imaginary numbers; those inputs return an error instead of a complex result. To find an exponent from base and result, both must be positive (so a real logarithm exists).