1

Pre-Algebra

Powers and Exponents

2

What Are You Learning?

• I CAN write powers as a product of the same factor and

• I CAN write products in exponential form.

• I CAN evaluate exponents.

3

Why Do You Need To Know This?

Exponents are used in the real-world to represent extremely large and small numbers. They are also used in solving problems.

4

Vocabulary Words

Factors—Two or more numbers multiplied together to form a product.

Example—2 • 3 = 6 The numbers 2 and 3 are

factors.

5

Vocabulary

Exponent—Number that tells how many times the base is used as a factor.

4²--2 is the exponent and it shows that 4 will be multiplied two times. 4 • 4

6

Vocabulary

Base—The common factor or number being multiplied.

5 • 5 • 5 • 5 • 5 Five is the base

7

Vocabulary

Powers—Numbers expressed using exponents

4² and 6³ are examples of powers.

4² is read “four to the second power.”

6³ is read “six to the third power.”

8

Vocabulary Squared—A number multiplied by itself

two times.

4 x 4 or 4² The four is being squared.

Cubed—A number multiplied by itself three times.

2 x 2 x 2 or 2³

9

Write Numbers in Exponential Form

Exponential Form—Numbers written with exponents.

Example 1—Write (-5)(-5)(-5) in exponential form.

-5 is the base. It is used as a factor 3 times. So, the exponent is 3.

(-5)(-5)(-5) = (-5)³

10

Write each expression in exponential form.

a. 6 · 6 · 6 b. (-3)(-3)(-3)(-3)

c. (-4n)(-4n)(-4n)(-4n)(-4n)

d. 4 · y · x · y · 3 · x · y

e. 9 · (p + 1)(p +1)

f. -5 · x · x · y · y · x

g. (a + 1)(a +1)(a +1)

11

Write each expression in exponential form.-8 • n • n • n • 4 • t

-32n

3t

-32

• 3n •

t

-8n3

+ 4

t

-32n

t3

25% 25%25%25%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33

1. -32n3t2. -32 • 3n • t3. -8n3 + 4t4. -32nt3

12

Vocabulary

Evaluate—Find the value of an expression.

Standard Form—Numbers written without exponents.

13

Write Powers in Standard Form

Evaluate each expression.

Example 1 -- 2 to the fifth power = 2 · 2 · 2 · 2 · 2 = 32

Example 2-- 4³ = 4 · 4 · 4 = 64

14

Evaluate each expression.

a. 7³

b. 52

c. (-4)³

d. -8²

e. 3 · 4²

f. 4² · 5³

g. 2³ · 5² · 7

h. 3 · 5² + 2³ · 3²

15

Evaluate.-32

-9 9 6 -6

25% 25%25%25%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33

1. -92. 93. 64. -6

16

Evaluate each expression

a. 5² · 8² · 3³

b. 9 · 6² · 2 · 3³

c. 3(2 • 2 + 5)²

d. 6² + 2(6) + 5

17

Evaluate. 12 - 42

-4

12

– 4

• 4 4

12

- 16

25% 25%25%25%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33

1. -42. 12 – 4 • 43. 44. 12 - 16

18

Determine whether each pair of expression is equivalent. Write yes or no.

a. 4ab2 and 4(ab)2

b. (2x)³ and 8x³

c. (mn)4 and m4 • n4

d. c³d³ and cd³

19

Compare using <, >, or =.a. 3³ 5²

b. 4³ 8²

c. 64÷8 2³

d. 4•10 102

e. -5³ -3°

f. 35 4³

g. -10³ (-10)³

h. 5² 23

i. 6³ 42

j. 24 4²

20

Class Work