PPT _Composite_ Week 29 dated 03-13-2023 Rational Exponents_.ppt

SEL Question
When your teachers ask how you are doing,
how many of them are really interested in your
answer - explain?
When you are in a bad mood, how
considerate and interested are your teachers
in trying to understand the reason why, calm,
support and help to pull you out of the bad
mood?

Do Now 03-13-2023
What is the set of all solutions to the
equation ?
A. B.
C. D. no solutions

UNIT 5
Exponential and Logarithmic Functions
Topic : A Real Numbers (N-RN.A.1, N-RN.A.2, N-Q.A.2, F-IF.B.6, F-BF.A.1a, F-LE.A.2)
Exploring: Rational Expressions
Eureka Module 3 Lesson 2 & 3 student edition.
N-RN.A.1, Explain how the definition of the meaning of rational exponents follows from
extending the properties of integer exponents to those values, allowing for a notation
for radicals in terms of rational exponents.
N-RN.A.2, Rewrite expressions involving radicals and rational exponents using the properties of
exponents.
N-Q.A.2, Define appropriate quantities for the purpose of descriptive modeling.

Objective
Students will be able to:
Students will be able to understand and
apply the properties of rational exponents
and radicals by simplifying expressions
and calculating quantities that involve
positive and negative rational exponents.

Essential Question
What are the properties of rational
exponents and how do apply these
properties to simplify expressions?

Learning Goals
1. Identify the properties of rational exponents
2. Write radicals as expressions raised to rational
exponents.
3. Simplify expressions with rational number
exponents using the rules of exponents.
4. Use rational exponents to simplify radical
expressions.
5. Convert between radicals and rational exponents.
6. Use the rules for exponents with rational
exponents.

Prerequisite Skills
• Before teaching rational expressions in Algebra 2, students should have a good understanding of the
following concepts:
• Algebraic expressions: Students should be able to identify variables, coefficients, and terms in
algebraic expressions. They should also be able to combine like terms and simplify expressions.
• Factoring: Students should know how to factor quadratic expressions using various methods such as
factoring by grouping, difference of squares, and trinomial factoring.
• Operations with fractions: Students should have a solid understanding of adding, subtracting,
multiplying, and dividing fractions, as well as simplifying fractions.
• Graphing linear equations: Students should know how to graph linear equations using slope-
intercept form, point-slope form, and standard form.
• Solving equations and inequalities: Students should be able to solve linear and quadratic equations,
as well as inequalities.
• Exponents and radicals: Students should understand the basic rules of exponents and be able to
simplify expressions involving radicals.
• Functions: Students should know how to evaluate functions, find the domain and range of functions,
and graph functions.
Having a strong foundation in these concepts will help students better understand rational expressions
and the operations that can be performed on them, such as simplifying, adding, subtracting,
multiplying, and dividing. It will also prepare them for more advanced topics in Algebra 2, such as
complex numbers and logarithms.

Handout
Monday March 13, 2023
See notes power point and cheat sheet in
Google classroom.
See videos posted in Google Classroom

Class-work for week 29
Week # 29
Graded during class-time and books will be checked
Monday 03-13-2023
• Eureka Students workbook, Module 3. Lesson 3: Rational Exponents
• Do for class-work:
• Opening Exercise a-f on page 17
• Example 1 a- c on page 18
• Complete exercise for home-work
Tuesday 03-14-2023
• Exercise 1 (a - d) on page 19
• Discussion questions on page 19
• Exercise 2-12 (# 1-12) on page 19

Classwork continued
Wednesday 03-15-2023
• Review homework
• Problem Set on page 22
• Complete Problem Set for home-work
Thursday 03-16-2023
• Eureka Students workbook, Module 3. Lesson 4: Properties of Exponents and Radials
• Opening Exercise a-d on page 27
• Example 1-3 on page 28
• Exercise 1-4 on page 29
Friday 03-17-2023
• Exercise 1-4 (# 1-4) on page 29
• Example 4 on page 30
• Exercise 5 & 6 on page 31

Class-work Practice
Available in Google Classroom & Mr. Lovemore
on Coppin Webpage.
Eureka Students workbook, Module 3,Lesson 3:
Rational Exponents
Do for class-work:
• Opening Exercise a-f on page 17
• Example 1 a- c on page 18

Level 3 Words
• Base
• Exponent
• Power
• Product rule
• Quotient rule
• Zero exponent
• Negative exponent
• Radicand
• Rationalization
• Radicals
• Numerator
• Denominator
• Inverse variation
• Complex fraction
• Common denominator

Definitions
• Base: The number or variable that is raised to a power in an exponential
expression.
• Exponent: The number that indicates how many times the base is multiplied
by itself in an exponential expression.
• Power: The result of an exponential expression.
• Product rule: A rule that states that when two exponential expressions with the
same base are multiplied, the exponents can be added.
• Quotient rule: A rule that states that when two exponential expressions with the
same base are divided, the exponents can be subtracted.
• Zero exponent: A rule that states that any non-zero base raised to the power of
zero equals one.
• Negative exponent:
A rule that states that any non-zero base raised to a negative
power is equal to the reciprocal of the base raised to the opposite
positive power.

Homework
Complete class work and
Continue working on problem set

Exit Ticket
Monday 03-13-2023
Please go to Google Classroom
and work on lesson 3 exit ticket..

Today’s Lesson
- Rational Exponents
- Fraction Exponents

Properties of Rational Exponents
a
a
a
n
m
n
m 


  a
a
mn
n
m 
  b
a
ab
m
m
m

0
,
1



a
a
a m
m
0
, 


a
a
a
a n
m
n
m
0
, 






 b
b
a
b
a
m
m
m

5
5
4
1
2
1
  

2
3
1
2
1
5
8
  

 4
1
4
4
3
2
7
3
1
7
2
3
1
3
1
4
12









• Do properties of exponents work for roots?
Same rules apply.
• What form must radical be in?
Fractional exponent form
• How do you know when a radical is in simplest
form?
When there are no more numbers to the root power as factors of the number under the
radical.
• Before you can add or subtract radicals what must
be true?
The number under the radicals must be the same.

23 Copyright © 2011 Pearson
Education, Inc.
Simplify.
a) 4
b)
c) 4
d)
 
2/3
8


1
4
1
4


24 Copyright © 2011 Pearson
Education, Inc.
Simplify.
a) 4
b)
c) 4
d)
 
2/3
8


1
4
1
4


Example 4
A. 216
B. 36
C. 18
D. 6

Example 3
A. 4
B. 8
C. 16
D. 32

Example 5A
Solve Exponential Equations
Solve 9x
= 729.

Example 5A
A. Solve 9x
= 729.
Answer: 3
9x
= 729 Original equation
9x
= 93
Rewrite 729 as 93
.
x= 3
Power Property of equality

Example 5B
B. Solve 162x – 1
= 8.

Example 5B
B. Solve 162x – 1
= 8.
162x – 1
= 8
Original equation
(24
)2x – 1
= 23
Rewrite 16 as 24
and 8 as 23
.
28x – 4
= 23
Power of a Power, Distributive
Property
8x – 4= 3
Power Property of Equality
8x = 7 Add 4 to each side.
Divide each side by 8.

Example 5A
Solve 93x + 1
= 274
.

Example 5A
Solve 93x + 1
= 274
.
A.
B.
C.
D. 2

Rewrite the roots in rational
form
Exponent Rule: When an exponent is raised
to an exponent – multiply the exponents
Exponent Rule: When the bases are the same
and the terms are being divided – subtract
the exponents
Since the original problem was in root
form, the answer needs to be in root form

How would we simplify this
expression?
What does the fraction exponent do to the
number?
The number can be written as a Radical
expression, with an index of the
denominator.
2
1
9

2
9

The Rule for Rational Exponents
4
64
64 3
3
1
1


n
n
b
b

What about Negative exponents
Negative exponents make inverses.
7
1
49
1
49
2
1
2
1




What if the numerator is not 1
Evaluate
5 2
5
2
32
32 

Evaluate
  5 10
5 2
5
5 2
5
2
2
2
32
32



Evaluate
 
4
2
2
2
32
32
2
5 10
5 2
5
5 2
5
2




For any nonzero real number b,
and integer m and n
Make sure the Radical express is real, no
b<0 when n is even.
 m
n
n m
n
m
b
or
b
b 

Simplify each expression
No fraction in the denominators.
3
2
7
4
7
1


x
y
y

Simplify
3
1
6
1
3
6
2
16
2
16


Simplify
3
1
6
4
3
1
6
1
4
3
1
6
1
3
6
2
2
2
)
2
(
2
16
2
16




Simplify
3
3
1
3
1
3
2
3
1
3
2
3
1
6
4
3
1
6
1
4
3
1
6
1
3
6
2
2
2
2
2
2
2
2
2
)
2
(
2
16
2
16









Simplify
6
4
6
1
6 4
4
4 x
x 

Simplify
  6
4
6
1
2
6
4
6
1
6 4
2
4
4
x
x
x



Simplify
 
6
4
6
2
6
4
6
1
2
6
4
6
1
6 4
2
2
4
4
x
x
x
x




Simplify
 
3
2
3
1
6
4
6
2
6
4
6
1
2
6
4
6
1
6 4
2
2
2
4
4
x
x
x
x
x





Simplify
 
  3 2
3
1
2
3
2
3
1
6
4
6
2
6
4
6
1
2
6
4
6
1
6 4
2
2
2
2
2
4
4
x
x
x
x
x
x
x







PPT _Composite_ Week 29 dated 03-13-2023 Rational Exponents_.ppt

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PPT _Composite_ Week 29 dated 03-13-2023 Rational Exponents_.ppt