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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

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**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:

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Examples:

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**Properties of Radicals**

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Simplify: Simplify:

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**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:

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

Example:

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Example:

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

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**Simplify each expression**

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

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