# 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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