Fractional Exponents: Everything You Need to Know
Are you ready to learn how to work with Fractional Exponents?
(Need help with Negative Exponents, click here for our super easy 3-step explanation)
Before you learn how to work with fractional exponents and use them to express powers and roots together, let's do a quick vocabulary review:
It is important that you are familiar with identifying the root index and radicand before moving forward.
Note: If a radical symbol does not include a root index value, the number 2 is implied (square root).
Example:
The radicand is 64 and the root index is 3. The left side of the equation implies “the cube root of 64”
What is a Fractional Exponent?
Now that you are able to identify the root index and the radicand, you are ready to understand fraction exponents.
A fractional exponent is another way of expressing powers and roots together.
You will now learn how to express a value either in radical form or as a value with a fractional exponent.
Example: Express the square root of 49 as a fractional exponent.
Note that we can rewrite 49 as 49^1 since they are equivalent (you will see in a minute why this is helpful)
In this case, the square root of 49 is equal to 49^(1/2) because they are both equal to 7.
But why?
Why is the square root of 49 equal to 49^(1/2)?
Fractional Exponents Rule
Here is the rule that you can use to work with fractional exponents from now on:
Now, let’s apply the above rule to two more examples:
Example A:
Example B:
Fractional Exponents Calculator
If you need a fast and easy way to convert between radical expressions and expressions with fractional exponents, then you can take advantage of the many free online fractional exponents calculators that are available.
This free fractional exponents calculator from www.calculatorsoup.com shares all of the steps involved in converting and also simplifies.
To use the fractional exponent calculator, simply input the base value, the value of the numerator and the value of the denominator and press calculate.
Are you looking to learn more about working with decimals and understanding place value? Click here for more free resources
Fractional Exponents Worksheet
Do you need more practice with learning how to work with fractional exponents? The following fractional decimals worksheet and answer key will give you plenty of opportunities to practice.
Click here to download your free Fractional Exponents Worksheet and Answers Key.
(answer key included)
And if you are looking for a more in-depth lesson on how to work with fractional exponents? Check out this awesome Fractional Exponents Explained! video lesson:
More Free Related Math Resources:
Keep Learning:
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By Anthony Persico
Anthony is the content crafter and head educator for YouTube's MashUp Math . You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.
