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Fractional Exponent Calculator — result sheet
Evaluate a base raised to a rational exponent, reduce the exponent fraction, show the equivalent root-power form, and reject non-real branches clearly.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a reduced rational exponent n/d, x^(n/d) = (d√x)^n = d√(x^n); a negative exponent is the reciprocal of the corresponding positive power.
The calculator reduces the exponent before applying the root rule, handles odd roots of negative bases in the real numbers, and refuses an even root of a negative base instead of returning a misleading NaN-like answer.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Base x — minimum -1000000000; maximum 1000000000
- Exponent numerator n — minimum -1000; maximum 1000
- Exponent denominator d — minimum 1; maximum 1000
Worked example
| Input | Value |
|---|---|
| Base x | 16 |
| Exponent numerator n | 3 |
| Exponent denominator d | 2 |
16^(3/2) = (√16)^3 = 64.
Assumptions and limits
- The result is requested over the real numbers; complex fractional powers are not generated.
- The exponent denominator is a positive integer and the base is finite.
- For a negative base, a real answer is allowed only when the reduced denominator is odd.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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