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 gt 0 and b gt 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 gt 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 gt 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.
11
(No Transcript)
12
(No Transcript)