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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

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:

Examples:

Properties of Radicals

Simplify: Simplify:

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:

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

Example:

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

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

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