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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
So, when we square
, we get 5. This means that
must be the square root of 5. Similarly,
Similarly
In general, for any positive number c, and any whole numbers n
and m (as long as m is not zero), we can write
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:
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