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Fractional Exponent - 22^(3⁄4)

Evaluate the following expression:


They say the answer is 10.158, but I do not understand.

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Aug 12, 2012
Fractional Exponent
by: Staff


A fractional exponent is a shorthand method which represents two mathematical operations: both an exponent and a root.

The numerator of the fractional exponent is the exponent. It shows how many times the base will be multiplied by itself.

The denominator of the fractional exponent is the root.

This is your expression:


This expression can also be written:


Your base is: 22

Your exponent is: 3

Your root is: 4 (the fourth root, which is the same as taking the square root twice)

You can evaluate your expression in two steps:

Step 1: The exponent (cube):


= 22*22*22

= 10648

Step 2: The root (4th root – take the square root twice)


= √(√(10648))

= √(103.1891467161155)

= 10.1582058807703

Check the root:

(10.1582058807703)* (10.1582058807703) * (10.1582058807703) * (10.1582058807703)

= 10648.000000000176, OK→ 10.1582058807703 is the 4th root.

>>> the final answer is:

22^(3⁄4) = 10.158

Thanks for writing.


Aug 14, 2012
Fractional Exponent
by: Anonymous

Wonderful explanation!! I can understand now! Thank you so much!!

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