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Exponents: Product to a Power and Quotient to a Power Rules, Exercises of Pre-Calculus

An explanation of the Product to a Power and Quotient to a Power rules for exponents. It includes examples and instructions for simplifying expressions. The document also mentions the absence of Sum to a Power and Difference to a Power rules.

What you will learn

  • How do you simplify expressions using these rules?
  • What are the Product to a Power and Quotient to a Power rules for exponents?
  • Why are there no Sum to a Power and Difference to a Power rules for exponents?

Typology: Exercises

2021/2022

Uploaded on 09/12/2022

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16-week Lesson 2 (8-week Lesson 1) Product to a Power and Quotient to a Power Rules for Exponents
1
Once again, please do not staple your
lecture notes together. There will be
days when I do not have time at the
end of class to give a regular quiz, so
I’ll simply have students submit a
page from their lecture notes. When
I do this, I will provide copies of the
page I take from your notes to
replace it, so you’ll still a have a
complete set of notes when you
leave. However it will be much
easier to remove one page and
replace it with another if your notes
are not stapled together. Instead, I
recommend keeping your lecture
notes for this course organized in a
three ring binder.
pf3
pf4
pf5

Partial preview of the text

Download Exponents: Product to a Power and Quotient to a Power Rules and more Exercises Pre-Calculus in PDF only on Docsity!

Once again, please do not staple your

lecture notes together. There will be

days when I do not have time at the

end of class to give a regular quiz, so

I’ll simply have students submit a

page from their lecture notes. When

I do this, I will provide copies of the

page I take from your notes to

replace it, so you’ll still a have a

complete set of notes when you

leave. However it will be much

easier to remove one page and

replace it with another if your notes

are not stapled together. Instead, I

recommend keeping your lecture

notes for this course organized in a

three ring binder.

Exponential Notation:

𝑛

  • the expression above is read “𝑥 to the power of 𝑛”, where 𝑥 is the

base and 𝑛 is the exponent

  • when the exponent 𝑛 is a positive integer, such as 1 , 2 , 3 , 4 , … ,

exponential notation represents the product of repeated factors (the

base times itself some number of times)

o anytime you have an exponent that is a positive integer you can

write the base that number of times

o another option is to use the rules we’ve covered so far (Product,

Quotient, and Power), or the rules we’re about to cover (Product

to a Power and Quotient to a Power)

Product to a Power Rule:

  • when a product is raised to a power, the exponent is distributed to

each factor (don’t forget the coefficients)

o

4

3

2

2

5

3

Example 1: Simplify each expression COMPLETELY.

a. − 9 𝑦

3

3

2

b. (

− 6

𝑦

2

𝑦

4

3

3

b.

For help using the

TI-30Xa calculator,

take a look at the

Calculator Tips

document in

Brightspace.

Example 2 : Simplify each expression COMPLETELY. Do NOT leave

negative exponents in your answers.

a. − 8 𝑦

2

3

4

b.

2

5

2

b.

c. (

1

2

4

6

5

d. (

2 𝑥

4

𝑦

7

3

−𝑥

5

2 𝑦

6

2

d.

8 𝑥

12

𝑦

21

𝑥

10

4 𝑦

12

8 𝑥

22

4 𝑦

33

𝟐𝒙

𝟐𝟐

𝒚

𝟑𝟑

e. (−

3

2

4

9

2

16

f. − (

5

4

3

1

2

6

125

64

1

64

125

64

1

64

124

64

𝟑𝟏

𝟏𝟔