Transcript 5.7 Rational Exponents

Algebra II
Mr. Gilbert
Chapter 5.7: Rational
Exponents
Standard & Honors
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Agenda

Warm-up (next slide)
– Check your answers
Lesson 9.2
 Questions and
comments

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Warm-up 5.7 (3 min.)
Use a calculator if you want

1.
2.
3.
4.
5.
6.
simplify these expressions:
(x2)(x3)
(62)(63)
(x2)3
(42)3
(-5x2y3)2
52/56
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Warm-up 5.7 (3 min.)
Use a calculator if you want

1.
2.
3.
4.
5.
6.
simplify these expressions:
(x2)(x3)
=
x5
(62)(63)
=
65
(x2)3
=
x6
(42)3
=
46
(-5x2y3)2
=
25x4y3
52/56
=
1/54
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Gravity: Newton and the Pirates
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5-7 Rational Exponents
Example 1 Radical Form (1)
Example 2 Exponential Form (2)
Example 3 Evaluate Expressions with
Rational Exponents (5)
Example 4 Rational Exponent with Numerator Other
Than 1 (3)
Example 5 Simplify Expressions with
Rational Exponents (2)
Example 6 Simplify Radical Expressions (5)
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Example 1 Definition
Write
Answer:
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in radical
form.
Definition of
7
Example 2 Definition
Write
Answer:
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using rational
exponents.
Definition of
8
Write
Answer:
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using rational
exponents.
Definition of
9
!
Technique
Evaluate
Method 1
Answer:
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Simplify.
10
!
Method 2
Power of a Power
Multiply exponents.
Answer:
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Evaluate
.
Method 1
Factor.
Power of a Power
Expand the square.
Find the fifth root.
Answer: The root is 4.
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Method 2
Power of a Power
Multiply exponents.
Answer: The root is 4.
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Evaluate each expression.
a.
Answer:
b.
Answer: 8
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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.
According to the formula, what is the maximum that
U.S. Weightlifter Oscar Chaplin III can lift if he weighs
77 kilograms?
Original formula
Use a calculator.
Answer: The formula predicts that he can
lift at most 372 kg.
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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.
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.
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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?
Answer: 380 kg
b. If he actually lifted 379 kg, compare this to the value
predicted by the formula.
Answer: The formula prediction is slightly higher than his
actual total.
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Simplify
.
Multiply by
Answer:
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18
Simplify each expression.
a.
Answer:
b.
Answer:
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Simplify
.
Rational exponents
Power of a Power
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Quotient of Powers
Answer:
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Simplify.
21
Simplify
.
Rational exponents
Power of a Power
Multiply.
Answer:
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Simplify.
22
Simplify
.
is the conjugate
of
Answer:
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Multiply.
23
Simplify each expression.
a.
Answer: 1
b.
Answer:
c.
Answer:
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Homework Review
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Homework
See Syllabus 5.7
pp. 261-262: 6,7, 21 - 63 multiples of 3
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Homework - Honors
See Syllabus 5.7
pp. 261-262: 21 - 66 (multiples of 3), 67-70
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