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Rational Exponents. Rational Exponents. Rational Exponents. Lesson 7 Contents. Example 1 Radical Form Example 2 Exponential Form Example 3 Evaluate Expressions with Rational Exponents Example 4 Rational Exponent with Numerator Other Than 1

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## Rational Exponents

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**Lesson 7 Contents**Example 1Radical Form Example 2Exponential Form Example 3Evaluate Expressions with Rational Exponents Example 4Rational Exponent with Numerator Other Than 1 Example 5Simplify Expressions with Rational Exponents Example 6Simplify Radical Expressions**Write in radical form.**Definition of Answer: Example 7-1a**Write in radical form.**Definition of Answer: Example 7-1b**Write each expression in radical form.**a. b. Answer: Answer: Example 7-1c**Write using rational exponents.**Answer: Definition of Example 7-2a**Write using rational exponents.**Answer: Definition of Example 7-2b**Write each radical using rational exponents.**a. b. Answer: Answer: Example 7-2c**Evaluate**Answer: Simplify. Example 7-3a**Evaluate .**Power of a Power Expand the square. Find the fifth root. Example 7-3c Answer: The root is 4.**Evaluate each expression.**a. b. Answer: Example 7-3e Answer: 8**Weight LiftingThe formula can be used toestimatethe**maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and theclean and jerk, combined. Original formula Use a calculator. Example 7-4a According to theformula, what is the maximum that U.S. WeightlifterOscar Chaplin III can lift if he weighs 77 kilograms? Answer:The formula predicts that he can lift at most 372 kg.**Weight LiftingThe formula can be used toestimatethe**maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and theclean and jerk, combined. Example 7-4b Oscar Chaplin’s total in the 2000 Olympics was 355 kg. Compare this to the value predicted by the formula. Answer:The formula prediction is somewhat higher than his actual total.**Weight LiftingUse the formula where M is the maximum total**mass that a weight lifter of mass B kilograms canlift. a. According to the formula, what is the maximum that a weight lifter can lift if he weighs 80 kilograms? b. If he actually lifted 379 kg, compare this to the value predicted by the formula. Example 7-4c Answer:380 kg Answer:The formula prediction is slightly higher than his actual total.**Simplify .**Multiply powers. Answer: Add exponents. Example 7-5a**Simplify .**Multiply by Example 7-5b**Answer:**Example 7-5c**Simplify each expression.**a. b. Answer: Answer: Example 7-5d**Simplify .**Rational exponents Power of a Power Example 7-6a**Quotient of Powers**Answer: Simplify. Example 7-6b**Simplify .**Rational exponents Power of a Power Multiply. Answer: Simplify. Example 7-6c**Simplify .**is the conjugate of Answer: Multiply. Example 7-6d**Simplify each expression.**a. b. c. Answer: Answer: Example 7-6e Answer: 1

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