Exponent Calculator: Powers & Fractions

When and How to Use the Exponent Calculator

Enter any two of base, exponent, and result to solve for the third. Trusted by students and educators for algebra and precalculus. Laws, definitions, and formulas are in the article below. All calculations run locally.

Workflow Tips

Solving for Result

Leave Result blank; enter base and exponent. Use the “Use e as base” button for natural exponentials.

Solving for Base

Enter exponent and result; leave Base blank. Works for positive result or negative result with an odd integer exponent.

Solving for Exponent

Leave Exponent blank; enter base and result (both positive). The tool solves for the exponent.

Negative and Fractional Exponents

Enter a negative exponent or a decimal (e.g. 0.5 for ½). The Learning insight shows the relevant law.

Exponent Calculator: Powers, Negative & Fractional Exponents

Free exponent calculator: calculate powers, negative exponents, and fractional exponents. Power of a power rules, how to find the base of an exponent, fractional exponent solver. Laws of exponents; solve for base, exponent, or result. Trusted by students and educators. No sign-up—all calculations run locally.

What This Calculator Does & Who It's For

Calculator Purpose & Ideal Users

What You'll Get:

Solve for result: aⁿ from base and exponent (including negative and decimal exponents). Solve for base: a from result and exponent—how to find the base of an exponent when you know the power and result. Solve for exponent: n from base and result (e.g. what exponent gives this power?). Use e as base: Button sets base to e (≈ 2.71828) for natural exponentials. Learning insight: Negative exponent law or natural exponential note when relevant. Expansion: For small positive integer exponents, shows the repeated multiplication (e.g. 2×2×2×2×2).
Ideal Users:

Students & algebra: Laws of exponents, calculate negative exponents, fractional exponent solver, power of a power rules. Teachers: Teaching module with laws and worked examples. Anyone: Quick power and nth root (base from result and exponent) calculations.
Scope & Limits:

Real numbers only; no imaginary results (e.g. negative base with non-integer exponent is not computed). Accepts positive/negative integers and decimals; fractional exponents entered as decimals. All calculations run in your browser; no data is sent to servers.

This exponent calculator solves for base, exponent, or result: enter any two, leave one blank.

What Is an Exponent? Exponentiation Definition

An exponent (or power) is the number of times a base is multiplied by itself. We write

a^n

(a to the power n), where a is the base and n is the exponent. By definition,

a^n = a \times a \times \cdots \times a

(n times) for positive integers n. When the exponent is 1, a¹ = a. For n = 0, a⁰ = 1 (when a ≠ 0). For negative exponents,

a^{-n} = \frac{1}{a^n}

For fractional exponents,

a^{p/q}

is the qth root of aᵖ (e.g. a^0.5 = √a). This exponent calculator computes aⁿ for real bases and exponents

Laws of Exponents: Product, Quotient, Power of a Power

Product rule: When multiplying same bases, add exponents:

a^n \times a^m = a^{n+m}

Quotient rule: When dividing same bases, subtract exponents:

\frac{a^m}{a^n} = a^{m-n}

Power of a power: When raising a power to a power, multiply exponents:

(a^m)^n = a^{m \times n}

Negative exponent:

a^{-n} = \frac{1}{a^n}

These power of a power rules and laws of indices are shown in the calculator’s Laws of exponents panel and in the Learning insight when they apply to your calculation

Power of a Product and Power of a Quotient

Power of a product:

(ab)^n = a^n b^n

—distribute the exponent to each factor. Power of a quotient:

(a/b)^n = a^n / b^n

—apply the exponent to numerator and denominator. These follow from the definition of exponentiation and the product rule. Use this exponent calculator to compute single powers

Exponent Calculator FAQ

? What happens when the exponent is 1?

When the exponent is 1, the result is the base itself: a¹ = a. For example, 5¹ = 5 and (−3)¹ = −3. This follows from the definition of exponentiation as repeated multiplication—multiplying the base once gives the base.

? How do you solve negative exponents?

A negative exponent means the reciprocal of the base raised to the positive exponent:

a^{-n} = \frac{1}{a^n}

For example, 2⁻³ = 1/8. Enter a negative exponent in this calculator to see the result and the Negative Exponent Law in the Learning insight

? Can an exponent be a decimal?

Yes. An exponent can be a decimal (fractional exponent). For example, 4^0.5 = √4 = 2, and 8^(1/3) = ∛8 = 2. The calculator accepts decimal exponents; for a negative base with a non-integer exponent the result would be complex, so this tool restricts to real results (e.g. positive base, or negative base with integer exponent).

? What is the base e in exponentiation?

e (Euler’s number, ≈ 2.71828) is the natural exponential base. eⁿ appears in growth, decay, and logarithms. Use the “Use e as base” button in this calculator to set the base to e and compute natural exponentials.

? How do I find the base of an exponent?

If you know the result and the exponent, the base is a = result^(1/n). Leave the Base field blank and enter the exponent and result; the calculator solves for the base. For a positive result, the base is the nth root of the result.

Exponent Calculator

Base, exponent & result

Expansion

Laws of exponents

Formulas used