Enter the base number and the index or root into the calculator to determine the value of the number with a fractional index. This calculator can also evaluate any of the variables given the others are known.

Fractional Index Formula

The following formula is used to calculate the value of a number with a fractional index.

V = a^{(1/n)}


  • V is the value of the number with a fractional index
  • a is the base number
  • n is the index or root

To calculate the value of a number with a fractional index, raise the base number to the power of the reciprocal of the index or root.

What is a Fractional Index?

A fractional index, also known as a rational exponent, is an exponent that is a fraction. It is used to represent both roots and powers of a number. The numerator of the fraction indicates the power to which the number is raised, while the denominator indicates the root of the number. For example, in the expression 2^(3/2), the number 2 is raised to the power of 3 and then the square root is taken.

How to Calculate Fractional Index?

The following steps outline how to calculate the Fractional Index using the formula: V = a^(1/n).

  1. First, determine the base number (a).
  2. Next, determine the index or root (n).
  3. Next, substitute the values of a and n into the formula V = a^(1/n).
  4. Finally, calculate the value of V.
  5. After inserting the variables and calculating the result, check your answer with a calculator.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Base number (a) = 4

Index or root (n) = 2