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.

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For example, to understand what means, notice that using the third of the laws of exponents described earlier, we can write

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So, when we square , we get 5. This means that must be the square root of 5. Similarly,

Similarly

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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: