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Interactive mathematics studio
Exponent Calculator
Calculate powers, solve for a missing base or exponent, and explore the result with exact forms, scientific notation, worked steps, a live graph and a value table.
Three solving modes · exact forms · graph · worked stepsWhat do you want to solve?
Live exponent result
Result
2⁸ = 256
Step-by-step solution
Exponential graph
The highlighted point shows the current exponent on y = aˣ. Drag the range or use the presets to compare growth and decay.
−8…8
Nearby exponent values
| Exponent | Result |
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Try a useful example
Recent calculations
Essential exponent rules
aᵐ · aⁿ = aᵐ⁺ⁿaᵐ ÷ aⁿ = aᵐ⁻ⁿ(aᵐ)ⁿ = aᵐⁿa⁰ = 1a⁻ⁿ = 1 ÷ aⁿa¹ᐟⁿ = ⁿ√aHow exponentiation works
In aᵇ, a is the base and b is the exponent. Positive integers mean repeated multiplication; negative exponents create reciprocals; fractional exponents represent roots.
Where powers are used
Exponents appear in compound growth, decay, scientific notation, geometry, computer science, physics, engineering and logarithmic equations.
Special cases and domain limits
The calculator distinguishes real and principal complex results. It also flags undefined cases such as zero raised to a negative power and treats 0⁰ as indeterminate rather than silently returning a misleading value.
Precision and very large values
Calculations use JavaScript floating-point arithmetic. Extremely large or small values are displayed in scientific notation, and rounded display values should not be mistaken for exact symbolic results.
Related mathematics tools
Continue with logarithms, roots or scientific notation using the related calculators.
Frequently asked questions
What is an exponent?
An exponent tells how a base is repeatedly multiplied, inverted or rooted.
How do negative exponents work?
A negative exponent creates a reciprocal: a⁻ⁿ = 1/aⁿ.
What does a fractional exponent mean?
A fractional exponent represents a root, such as a¹ᐟ² = √a.
Can the calculator solve for the exponent?
Yes. For a positive base other than 1 and a positive result, it uses logarithms: b = ln(result)/ln(base).
Can a negative base have a fractional exponent?
It may not have a real value; the calculator shows the principal complex result when appropriate.
What is zero to the zero power?
Its value depends on context, so this calculator labels 0⁰ as indeterminate.
Why is scientific notation shown?
It keeps very large and very small results readable.
Can I share a calculation?
Yes. The share button creates a URL containing the current mode and values.