INTRO TO EXPONENTS

1

Write each expression using exponents

1. !

2. !

3. !

4 ⋅ 4 ⋅ 4 ⋅ 4 ⋅ 4

y ⋅ y ⋅ y

6 ⋅ 6

4. !

5. !

6. !

b ⋅ b ⋅ b ⋅ b ⋅ b ⋅ b

13

⋅13

⋅13

⋅13

⋅13

⋅13

⋅13

⋅13

xy

⋅xy

⋅xy

⋅xy

⋅wz

⋅wz

2

Write each expression using exponents

1. !

2. !

3. !

5 ⋅ 5 ⋅ 5 ⋅ 5 + x ⋅ x ⋅ x

y ⋅ y ⋅ z ⋅ z − 3 ⋅ 3 ⋅ 3 ⋅ 3

x ⋅ x ⋅ p ⋅ z ⋅ y ⋅ y + 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 2 ⋅ 2 ⋅ x ⋅ x

3

Evaluate each expression

1. !

2. !

3. !

23

( 23 )

2

−23

2

4

Find the area or volume

1.

2.

2m

5cm

7cm 3cm

5

PROPERTIES OF EXPONENTSPART 1

6

VOCABULARY

Monomial:

Constant:

Factor:

7

VOCABULARY CONTINUED…

xn

8

Identify/Determine whether each expression is a monomial and explain

(a.) �

(b.) �

(c.) �

15

x + 7

w3

(d.) �

(e.) �

(f.) �

y

12 − x

wxyz

9

Write out each in expanded form, then rewrite using exponents

1. !

2. !

32 ⋅ 36

43 ⋅ 45

10

Product of Powers

To multiply two powers with the same base, add their exponents

General rule:

11

Example 1: Simplify Each Expression

(a.) �

(b.) �

(3y4)(7y5)

( − 4rx2t3)( − 6r5x2t)

12

Example 1: Simplify Each Expression

(c.) �

(d.) �

( − xy3)(xz)

( 12

x2y)( 13

wz)

13

PROPERTIES OF EXPONENTSPART 2

14

Write out each in expanded form, then rewrite using exponents

1. !

2. !

(32)5

(w4)3

15

Power of a Power

To raise a power to an exponent, multiply the exponents

General rule:

16

Write out each in expanded form, then rewrite using exponents

(a.) �

(b.) �

(2x)2

(3xyz2)3

17

Power of a ProductTo find the power of a product, find the power of each factor and multiply

General rule:

18

Example 1: Simplify Each Expression

(a.) �

(b.) �

( − xy)3(xz)

(2a3b2)(b3)2

19

Example 1: Simplify Each Expression

(c.) �

(d.) �

(2xy)2( − 3x2)(4y4)

(25a2b3)( 15

abf)2

20

PROPERTIES OF EXPONENTSPART 3

21

Write out each in expanded form, then rewrite using exponents

(a.) �

(b.) �

27

24

g8

g5

22

Quotient of PowersWhen dividing powers with the same base, subtract the exponents and keep the base

General rule:

23

Example 1: Simplify Each Expression

(a.) �

(b.) �

g3h5

gh2

k7m10pk5m3p

24

Power of a QuotientWhen raising a quotient to a power, distribute the exponent to both the numerator and the denominator

General rule:

25

Example 1: Simplify Each Expression

(a.) �

(b.) �

( 3p3

7 )2

( 4x3

5y4 )3

26

Zero Exponent Property

Any base, except 0, raised to an exponent of 0 equals 1

General rule:

27

Example 1: Simplify Each Expression

(a.) �

(b.) �

( 4n2q5r2

9n3q2r )0

b4c2d0

b2c

28

PROPERTIES OF EXPONENTSPART 4

29

Simplify using expanded form and then properties of exponents

�c2

c5 �c2

c5

30

Negative Exponent Property

General rule:

31

How do you know when an expression is simplified?

When…

1.

2.

3.

4.

32

Example 1: Simplify Each Expression

(a.) � n−5p4

r−2

33

Example 1: Simplify Each Expression

(b.) �5r−3t4

−20r2t7u−5

34

Example 1: Simplify Each Expression

(c.) �( 3x2y−3z2x−2y3z2 )

2

35