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Algebra · Exponents

Powers, Radicals & Logarithms Calculator

Evaluate real powers, indexed radicals, and logarithms while checking domains and explaining their inverse relationships.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Real-valued exponent, radical, and logarithm operations with domain checks

Power

aⁿ

Radical

ⁿ√a = a¹⁄ⁿ

Logarithm

logᵦ(x)=y ⇔ bʸ=xx>0, b>0, b≠1
Algebra · Exponents

Evaluate powers, radicals, and logarithms

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

aⁿ

Choose an operation and enter values inside its real-number domain.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Calculations are restricted to real finite results. Even roots require a non-negative radicand; logarithm arguments must be positive and logarithm bases must be positive and different from one.

Worked examples

See the method in practice

01

Cube root of a negative number

The cube root of −27 is −3 because an odd root preserves the sign and (−3)³ = −27.

02

Binary logarithm

log₂(8) = 3 because 2³ = 8.

Questions

Frequently asked

Why is an even root of a negative number rejected?

It has no real value; supporting it would require complex-number output.

Why can a logarithm base not equal one?

Every power of one equals one, so it cannot define a one-to-one exponential function.

Are irrational results exact?

They are computed at full floating-point precision and displayed to at most three decimals.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax College Algebra — Exponential and Logarithmic Functions

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology