Sullivan Algebra and Trigonometry: Section R.8 nth Roots, Rational Exponents

1. Sullivan Algebra and Trigonometry: Section R.8nth 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. Express the answer so only positive exponents occur.