TutorEye explains Fractional indices/exponents for you

Attention Algebra Students - Exponents/Indices can be fractions too!

Now that you know how to calculate the squares, cubes, etc. figure out how to calculate fractional exponents powers.

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Definition of Fractional Exponents:


A fractional exponent is a way of combining powers and roots in a single expression.

A fractional exponent has the following general form:

n/m = (m√b) n = m √ (b n)


Top things to learn under Fractional Exponents/Indices from the online tutor

  • What are fractional indices?
  • How to use fractional indices?
  • How to solve fractional indices?
  • How to multiply Fractional Exponents with the Same Base
  • How to divide Fractional Exponents
  • Negative fractional exponents


Fractional Exponents Frequently Asked Questions:

Question 1: How to calculate fractional exponents?

To calculate the fractional exponent we check the fraction given in power form. Then, break the fraction n/m in two terms

  1. n, as a whole number and,
  2. 1/m, as a fraction


Then the fraction part changes to mth root of that number and n is its power.

n/m = (m√b) n = m √ (b n)


5/3 = (5^5)5/3 = 3√(5^5) = 5 x  3√(5^2) = 53√25


Question 2: How to multiply fractional exponents?


Multiplying words with the same base and fractional exponents is the same as adding the exponents together.


51/2 x 53/2 = 51/2+3/2 = 54/2 = 52 = 25


Question 3: How to work out negative fractional indices?

To solve the negative exponent fraction indices we use the following rule x-nm=1xnm=1mxn.



2-5/2 = 1/(2)5/2 = 1/√25 = 1/(2x2x√2) = 1/(4√2)


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