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Algebra IIAlgebra IIMr. GilbertMr. Gilbert

Chapter 5.7: Rational Chapter 5.7: Rational ExponentsExponents

Standard & HonorsStandard & Honors

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AgendaAgenda

Warm-up (next slide)Warm-up (next slide)– Check your answersCheck your answers

Lesson 9.2Lesson 9.2 Questions and Questions and

commentscomments

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Warm-up 5.7 (3 min.)Warm-up 5.7 (3 min.)

Use a calculator if you wantUse a calculator if you want simplify these expressions:simplify these expressions:

1.1. (x(x22)(x)(x33))

2.2. (6(622)(6)(633))

3.3. (x(x22))33

4.4. (4(422))33

5.5. (-5x(-5x22yy33))22

6.6. 5522/5/566

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Warm-up 5.7 (3 min.)Warm-up 5.7 (3 min.)

Use a calculator if you wantUse a calculator if you want simplify these expressions:simplify these expressions:

1.1. (x(x22)(x)(x33)) == xx55

2.2. (6(622)(6)(633)) = = 6655

3.3. (x(x22))33 == xx66

4.4. (4(422))33 == 4466

5.5. (-5x(-5x22yy33))22 == 25x25x44yy33

6.6. 5522/5/566 == 1/51/544

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Gravity: Newton and the PiratesGravity: Newton and the Pirates

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Example 1 Radical Form (1)

Example 2 Exponential Form (2)

Example 3Evaluate Expressions with Rational Exponents (5)

Example 4Rational Exponent with Numerator Other Than 1 (3)

Example 5Simplify Expressions with Rational Exponents (2)

Example 6 Simplify Radical Expressions (5)

5-7 Rational Exponents

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Write in radical form.

Answer: Definition of

Example 1 Definition

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Write using rational exponents.

Definition of Answer:

Example 2 Definition

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Write using rational exponents.

Definition of Answer:

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Evaluate

Method 1

Answer: Simplify.

! Technique

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Multiply exponents.

Method 2

Answer:

Power of a Power

!

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Answer: The root is 4.

Evaluate .

Method 1 Factor.

Power of a Power

Expand the square.

Find the fifth root.

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Answer: The root is 4.

Power of a Power

Multiply exponents.

Method 2

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Evaluate each expression.

a.

b.

Answer: 8

Answer:

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According to the formula, what is the maximum that U.S. Weightlifter Oscar Chaplin III can lift if he weighs 77 kilograms?

Answer: The formula predicts that he can lift at most 372 kg.

Weight Lifting The formula can be used to estimate the maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and the clean and jerk, combined.

Original formula

Use a calculator.

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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 Lifting The formula can be used to estimate the maximum total mass that a weight lifter of mass B kilograms can lift in two lifts, the snatch and the clean and jerk, combined.

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Answer: 380 kg

Answer: The formula prediction is slightly higher than hisactual total.

Weight Lifting Use the formula where M is the maximum total mass that a weight lifter of mass B kilograms can lift.

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 valuepredicted by the formula.

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Simplify .

Multiply by

Answer:

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Simplify each expression.

a.

b.

Answer:

Answer:

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Simplify .

Rational exponents

Power of a Power

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Quotient of Powers

Answer: Simplify.

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Simplify .

Rational exponents

Power of a Power

Answer: Simplify.

Multiply.

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Answer: Multiply.

Simplify .

is the conjugate

of

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Answer: 1

Simplify each expression.

a.

b.

c. Answer:

Answer:

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Homework ReviewHomework Review

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HomeworkHomework

See Syllabus 5.7

pp. 261-262: 6,7, 21 - 63 multiples of 3

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Homework - HonorsHomework - Honors

See Syllabus 5.7

pp. 261-262: 21 - 66 (multiples of 3), 67-70