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Fractional Power from Numerator and Denominator

Fractional Power from Numerator and Denominator. Evaluate a real power or principal root, with reverse inputs where a unique solution exists.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Power result = 8.

Result = base^(numerator / denominator)

Worked example

Enter these known values and leave the other values blank.

Nonnegative base
16
Exponent numerator
3
Nonzero exponent denominator
4
Power result
8

Assumptions and limitations

  • Arithmetic uses 64 significant decimal digits, with separate rounding for displayed results. Very large integer arithmetic is not an exact arbitrary-length integer service.
  • The base is nonnegative and the exponent denominator must be nonzero. A zero base requires a positive exponent.
  • The output is a power value, not a simplified symbolic fraction. Inverse inputs use logarithms or principal powers and can be indeterminate when the base or result equals zero or one.

Common questions

Can I enter the result to calculate a missing input?

The retained inverse rules solve from sufficient known inputs. Roots and inverse trigonometric functions use principal values; indeterminate inputs do not have a unique solution.

References

Bookify rejects undefined zero powers or zero root/exponent denominators and validates real-valued powers while preserving the captured equations and inverse rules.

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