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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:  