1. Sullivan Algebra and Trigonometry: Section R
Sullivan Algebra and Trigonometry: Section R.8 nth Roots, Rational Exponents
Objectives of this Section
Work with nth Roots
Simplify Radicals
Rationalize Denominators
Simplify Expressions with Rational Exponents

2. The principal nth root of a real number a, symbolized by is defined as follows:
where a > 0 and b > 0 if n is even and a, b are any real numbers if n is odd
Examples:

3. Examples:

4. Properties of Radicals

5. Simplify:
Simplify:

6. If a is a real number and n > 2 is an integer, then
Note that rational exponents are equivalent to radicals. They are a different notation to express the same concept.
Example:

7. If a is a real number and m and n are integers containing no common factors with n > 2, then
Example:

8. Example:

9. When simplifying expressions with rational exponents, we can utilize the Laws of Exponent.

10. Simplify each expression
Simplify each expression. Express the answer so only positive exponents occur.