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Rational (fractional)
exponents are an alternate way to express roots!
We're talking radicals here! |
Notice:
The denominator of the rational exponent
becomes the index of the radical,
and the numerator becomes the exponent of the radicand (expression inside
the radical).
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When you are dealing
with a radical
expression,
you can convert it to an expression
containing a rational (fractional) power. This conversion may
make the problem easier to solve. |
Specifically,  , or in
general:
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We have already discussed simplifying
radicals such as:
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or |
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Let's look at these two problems in a new
light! When asked to simplify these radicals, it is often
easier to rewrite the
radicals using rational exponents and solve
the problems by dealing with the laws of
exponents.
Notice how applying the rules for dealing with the
exponents makes quick work of the variables.
Look at these examples:
When dealing with rational exponents, the Rules for Exponents
are still valid!!!
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Rationalizing radical denominators
may often be accomplished more easily by using rational exponents.
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Look at this example,
solved two ways. |
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Simplify:
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Solved by Rationalizing the
Denominator |
Solved by Using Rational
Exponents |
Check out how these problems are done using rational exponents:
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