TUTORIALS:
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Fractional Exponents
Not only can we create a useful definition for what a negative
exponent means (see the previous document in these notes), but we
can even find a useful definition for exponents which are
fractions.
For example, to understand what
means, notice that using the third of the laws of exponents
described earlier, we can write
![](./articles_imgs/547/pic2.gif)
So, when we square
, we get 5. This means that
must be the square root of 5. Similarly,
![](./articles_imgs/547/pic3.gif)
Similarly
![](./articles_imgs/547/pic4.gif)
In general, for any positive number c, and any whole numbers n
and m (as long as m is not zero), we can write
![](./articles_imgs/547/pic5.gif)
More information about roots is given in a later section of
these notes. This way of understanding exponents which are
fractions is consistent with all the laws of exponents that have
been described in these notes.
examples:
![](./articles_imgs/547/pic6.gif)
![](./articles_imgs/547/pic7.gif)
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