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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 x3 = 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. 