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Fractional Exponents

When you have an exponent that is a fraction, you are really seeing the inverse operation of the exponent. Just like addition cancels subtractions, and multiplication cancels division, roots cancel exponents.

Let's take a look at one now:

This can actually be rewritten as a square root:

How did we find that? If you have a fraction in the exponent, simply move the denominator (the bottom number) into a square root, and leave the numerator as an exponent of the base. (In our example, the "numerator is an exponent of the base" and would be written as 4¹, which is equal to 4!

Here is a more complex example:

Using our above description, we move the denominator to the exponent outside of a square root sign, and leave the rest:

We can simplify (solve) the inner exponent:

Using a calculator to find the exact value, it is equal to 2.27950706.

Pretty simple, aren't they?

Find another math lesson at the Math Lesson and Tutorial Center!

 

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