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rational exponents
Math D : 7.2
We de ne rational exponents to have the same properties as
integer expo
nents. Suppose
so x^{3} = 7 so x is the number whose cube is 7 so
But we started with
De nition 0.1 If
represents a real number and n 2 is an integer ,
then
If a is negative , n must be odd.
Example 0.1 Converting from
De nition 0.2 If
represents a real number , m/n is a positive rational
number reduced to lowest terms , and n ≥ 2 is an integer, then
and
Example 0.2 Converting to
De nition 0.3 If is a nonzero real number , then
Example 0.3 Negative exponents
Property 0.1 Properties of Rational Exponents
If m and n are rational exponents , and a and b are real numbers for which
the following expressions are de ned, then
Example 0.4 Properties of Rational Exponents and Reducing
Property 0.2 Simplifying Rational Expressions
•Rewrite each radical expression with a rational exponent.
• Simplify using properties of rational exponents.
•Rewrite in radical notation .
Example 0.5 Simplify
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