Download - Algebra II Mr. Gilbert
04/19/2304/19/23 11
Algebra IIAlgebra IIMr. GilbertMr. Gilbert
Chapter 5.7: Rational Chapter 5.7: Rational ExponentsExponents
Standard & HonorsStandard & Honors
04/19/2304/19/23 22
AgendaAgenda
Warm-up (next slide)Warm-up (next slide)– Check your answersCheck your answers
Lesson 9.2Lesson 9.2 Questions and Questions and
commentscomments
04/19/2304/19/23 33
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
04/19/2304/19/23 44
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
04/19/2304/19/23 66
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
04/19/2304/19/23 1212
Answer: The root is 4.
Evaluate .
Method 1 Factor.
Power of a Power
Expand the square.
Find the fifth root.
04/19/2304/19/23 1515
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.
04/19/2304/19/23 1616
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.
04/19/2304/19/23 1717
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.