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Rational Powers in Real Arithmetic

Rational Powers in Real Arithmetic. 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^exponent

Worked example

Enter these known values and leave the other values blank.

Base
16
Exponent
.75
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.
  • Forward evaluation permits a negative base for integer exponents. Noninteger powers of a negative base are outside this real-number model.
  • A zero base requires a positive exponent; zero to a nonpositive exponent is rejected.
  • Inverse base calculation returns a principal root. Exponent inversion uses logarithms and requires positive values and a base different from one. Multiple or indeterminate inverse solutions are not enumerated.
  • The retained source result bound is less than 10^2000. Displayed values are rounded independently of the internal arithmetic.

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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