Free Exponent Calculator With Powers, Roots, Fractional Exponents, and Step-by-Step Work

Evaluate a base raised to an exponent, interpret negative and fractional exponents, view scientific notation, and compare the result with reciprocal or root forms.

Browser-basedNo sign-upPrivate local historyStep-by-step

Interactive calculator

Base (a)

Exponent (b)

Result—

Scientific notation—

Reciprocal—

Enter a base and exponent.

How to use it

Enter a numeric base and exponent.
Use fractional decimal exponents only when the real-valued result is defined.
Calculate to see standard and scientific forms.
Review the exponent-rule interpretation.
For negative bases with non-integer exponents, use a complex-number tool instead.

What this calculator includes

1. Power evaluationCompute base raised to a real exponent.

2. Negative exponentsShow reciprocal interpretation.

3. Fractional exponentsConnect powers to roots.

4. Integer expansionShow repeated multiplication for manageable integers.

5. Scientific notationDisplay large and small results compactly.

6. Reciprocal viewShow 1/result when defined.

7. Root interpretationExplain 1/n powers.

8. Magnitude estimateReport base-10 order of magnitude.

9. Special casesHandle zero, one, and negative bases cautiously.

10. Step breakdownDisplay the chosen exponent rule.

11. HistoryStore recent expressions locally.

12. Copy/downloadExport the result and explanation.

Result checklist

0 / 5 complete

Inputs use the intended units or interpretation.The formula mode matches the problem.The result magnitude is reasonable.I reviewed the shown calculation steps.I will round only at the final step.

Local calculation history

Formula and reference table

Rule	Identity	Example
Product of powers	a^m × a^n = a^(m+n)	2³×2² = 2⁵
Negative exponent	a^-n = 1/a^n	2^-3 = 1/8
Fractional exponent	a^(1/n) = n-th root of a	16^0.5 = 4
Power of a power	(a^m)^n = a^(mn)	(2³)² = 2⁶

Quick knowledge check

What does a negative exponent do for a nonzero base?

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Frequently asked questions

Can exponents be negative?

Yes. A negative exponent represents the reciprocal of the corresponding positive power.

Can exponents be fractions?

Yes. Fractional exponents correspond to roots and combinations of roots and powers.

Why can a negative base fail with a decimal exponent?

Some fractional powers of negative numbers are complex, while JavaScript numeric arithmetic here is limited to real-number output.

What is scientific notation?

It represents a value as a coefficient multiplied by a power of ten.

Scope and accuracy

Results use standard browser floating-point arithmetic. Extremely large or tiny values can overflow, underflow, or lose precision, and complex-valued exponentiation is outside this calculator.