# Warm-up. Wed. Jan 26

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Warm-up. Wed. Jan 26. Simplify Completely. No zero or negative exponents 1. 2. Review. Recall: To solve a quadratic equation like the following, use a square root method:. Goal for this lesson: Radical equation such as:. Review: Laws of Exponents. - PowerPoint PPT Presentation

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Warm-up. Wed. Jan 26Recall:ExponentPROPERTIESaman = am+n(am)n = amn(ab)n = an bnam/an = am-n

Simplify Completely. No zero or negative exponents

1.

2.

1Review

Recall: To solve a quadratic equation like the following, use a square root method:Goal for this lesson: Radical equation such as:

2Review: Laws of Exponents

3Section A.9 nth Roots; Rational Exponents; Radical Equationsnth RootEvaluating nth rootsProperties of nth rootsSolving Radical EquationsRationalize Denominators

Fractional ExponentsSimplifying Fractional ExponentsSimplifying radicals using rational exponentsSimplify radicals some more2 methodsMore practice

41. nth Roots

cubed root of 8 is 2

DefinitionThe principal nth root of a number is defined as:

52. Evaluating nth Roots

1)

2)

3)63. Properties of nth Roots

Product Rule for nth RootsQuotient Rule for nth Roots73 a) Practice simplifying radicals

83 b) Multiplying and Combining Radicals

1)

Solve the following equation.Isolate radical to one side of equationRaise both sides to power equal to index of radicandCheck for extraneous solutions104. Solving Equations with Roots

Solve the following equation.Isolate radical to one side of equationRaise both sides to power equal to index of radicandCheck for extraneous solutions114. Solving Equations with Roots

Solve the following equation.12Goal: Remove radicals in the denominators5. Rationalizing Denominators

Key Idea: For a denominator of the form Multiply numerator and denominator by:

136. Fractional Exponents

If a is a real number and is an integer, then

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

146 a) Simplifying Fractional ExponentsSimplify the following expressions.

1)

2)156 b) Simplifying Fractional ExponentsSimplify the following expressions.

166 c) Practice simplifying radicals using rational exponents

Examples.Rewrite each radical using rational exponents and simplify.17Day 2: Warm-up

Solve the following formula for V:Solve the following formula for A:

Simplify:187. a) Simplify Radicals 2 methodsMethod 1: Look for powers of each term that match the root.

Method 2:Rewrite using rational exponents and simplify.