# Fraction Exponents Calculator

## Calculator Use

Use this calculator to find the fractional exponent of a number x. With fractional exponents you are solving for the d^{th} root of the number x raised to the power n. For example, the following are the same:

\( 4^{\frac{3}{2}} = \sqrt[2]{4^{3}} \)

and since 4 cubed equals 64 we get

\( = \sqrt[2]{64} = \pm 8 \)

## Notes on Fractional Exponents:

This online calculator puts calculation of both exponents and radicals into exponent form.

- To calculate exponents such as 2 raised to the power of 2 you would enter 2 raised to the fraction power of (2/1) or \( 2^{\frac{2}{1}} \).
- To calculate radicals such as the square root of 16 you would enter 16 raised to the power of (1/2).
- To calculate combined exponents and radicals such as the 4th root of 16 raised to the power of 5 you would enter 16 raised to the power of (5/4) or \( 16^{\frac{5}{4}} \) where x = 16, n = 5 and d = 4.
- If you try to take the root of a negative number your answer may be NaN = Not a Number.

For more detail on Exponent Theory see Mathworld Exponent Laws.

**Cite this content, page or calculator as:**

Furey, Edward "Fraction Exponents Calculator"; from *https://www.calculatorsoup.com* - Online Calculator Resource.