Fraction Exponent Calculator

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Just below is a fraction exponent calculator. In this tool, raise a base to the power of a fraction, n/d or numerator over denominator.

Also try our regular exponent calculator.

Fraction Exponents Calculator

Raising a Number to a Fraction

When you raise a base number to a power, you multiply the base by itself power number of times. However, since a fraction isn't (generally) a whole number, the result is a bit trickier.

Raising a base to a fraction means to raise a base number to the numerator power, then take the denominator root of that number. The formula for raising to a fractional exponent is:


Note this identity also shows how to convert between exponents and roots. For example, taking the square root of the number is the same as raising it to the 1/2.

As usual though, it's easiest to walk through an exponent calculation to get a feel for the operation.

Example Fractional Exponent Calculation

Let's say you need to raise the number 729 to the 2/3 power.

729^{\frac{2}{3}}=\sqrt[3]{729^2}\\~\\\sqrt[3]{531441 }=81

How to Use the Fraction Exponents Tool

This one can get tricky – that's why it's useful to have the tool.

In the Base box, enter the number which you will raise to the fraction. Then in the Fraction boxes below for numerator and denominator, enter your fraction.

Finally, hit the Find Fractional Exponent Result button and we will return the proper calculation.

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PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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