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Objective

Use powers and exponents in expressions

Vocabulary

Exponent

The number of times the base is used as a factor

34

4 is the exponent telling you to multiply the base (3) times itself four times

3 · 3 · 3 · 3

Vocabulary

Base

The number used as a factor

34

3 is the base and you will multiply it times itself (factor)

3 · 3 · 3 · 3

Vocabulary

Power

Number expressed using exponents

34

Three to the power of 4

3 · 3 · 3 · 3

Vocabulary

Squared

The exponent representing the power of 2

32

This is read “three squared”

3 · 3

Vocabulary

Cubed

The exponent representing the power of 3

33

This is read “three cubed”

3 · 3 · 3

Example 1 Write Powers and Products

Example 2 Write Powers and Products

Example 3 Use Powers to Solve a Problem

Example 4Write Prime Factorization Using Exponents

Write using an exponent. Then find the value of the power.

Write the problem

Since 5 is repeated with multiplication , write it as the base

1/4

5 5 5 5

5

The 5 is repeated four times, so write the exponent as 4

4

Now solve using the calculator

Write using an exponent. Then find the value of the power.

Answer: 625

yx

The base is 5 so put 5 in the calculator

Push the yx key on the calculator

1/4

5 5 5 5

5

The exponent is 4 so put 4 in the calculator

4

Push the = sign on the calculator

5

4 =

Write using an exponent. Then find the value of the power.

1/4

47 Answer: ; 16,384

Write as a product. Then find the value of the product.

Answer: 512

First write the product which means use multiplication signs

Write problem

2/4

83

The base is 8 so it will be repeated

The exponent is 3 so repeat the 8 three times

Now solve using the calculator

Write as a product. Then find the value of the product.

2/4

Answer: 6 6 6 6 ; 1,296

Answer: 4,096 meters.

ELEVATIONS The highest point in Utah is King’s Peak. It stands just a bit higher than meters. What is this elevation?

Write problem46

Use calculator to solve

3/4

SWIMMING POOL The length of a new swimming pool being built at the community recreation center is listed as feet. What is the length of the new pool?

3/4

Answer: 64 feet

Write the prime factorization of 126 using exponents.

4/4

126 Write the number

Draw prime factorization brackets

Decide on a prime number that will go evenly into 126

The one’s digit is 6 which is divisible by 2

Place the prime number 2 to the left of the bracket

2

Write the prime factorization of 126 using exponents.

4/4

1262 Divide 126 by 2 and place the answer below the bracket

63

Determine if 63 is a prime number

Since 63 is not an even number, try the divisibility rule for the prime number 3

6 + 3 = 9 and 9 is divisible by 3 so 63 is divisible by 3

Write the prime factorization of 126 using exponents.

4/4

1262

63

63 is not prime so place another prime factorization bracket under 63

Since 63 is divisible by 3, place the 3 to the left of the bracket

3

Divide 63 by 3 and place the answer below the bracket

21

Determine if 21 is a prime number

Write the prime factorization of 126 using exponents.

4/4

1262

633

21

Since 21 is not an even number, try the divisibility rule for the prime number 3

2 + 1 = 3 and 3 is divisible by 3 so 21 is divisible by 3

21 is not prime so place another prime factorization bracket under 21

Since 21 is divisible by 3, place the 3 to the left of the bracket

3

Write the prime factorization of 126 using exponents.

4/4

1262

633

213

Divide 21 by 3 and place the answer below the bracket

7Determine if 7 is a prime number

The factors of 7 are 1 and 7

7 fits the definition of a prime number

Finished prime factoring so now write answer using exponents

Write the prime factorization of 126 using exponents.

4/4

1262

633

2137

Write the smallest prime number which in this case is 2

2

Circle all the 2’s that were used in prime factoring, counting as you go

Since there is only 1 two , do not put an exponent

Write the prime factorization of 126 using exponents.

4/4

1262

633

2137

2

Next put a multiplication sign

Note: Do not use “x” for multiplication

Write the next smallest prime number which in this case is 3

Circle all the 3’s that were used in prime factoring, counting as you go

3

Write the prime factorization of 126 using exponents.

4/4

1262

633

2137

2

Since there are 2 threes , put an exponent of 2

32

Next put a multiplication sign

Write the next smallest prime number which in this case is 7

7

Write the prime factorization of 126 using exponents.

4/4

1262

633

2137

2 32 7

Circle all the 7’s that were used in prime factoring, counting as you go

Since there is only 1 seven , do not put an exponent

Answer:

Write the prime factorization of 144 using exponents.

*

4/4

Answer: 24 32

Assignment

Lesson 1:4 Powers & Exponents 11 - 34 All