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8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x...

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8.3 – Multiplying Exponents 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 • 2 • 2 2. x • x • x • x 3. Write each expression without using an exponent. 4. 4 3 5. y 2 6. m –4 2 3 4 • 4 • 4 y • y
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Page 1: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

8.3 – Multiplying Exponents8.3 – Multiplying ExponentsWarm Up

Write each expression using an exponent.1. 2 • 2 • 2

2. x • x • x • x

3.

Write each expression without using an exponent.

4. 43

5. y2

6. m–4

23

4 • 4 • 4

y • y

Page 2: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Lesson #8.3Multiplying Exponents

Objective: SWBAT multiply powers.

Concept: Unit 8

Page 3: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Given Think of it like this:

x * x * x * x * x * x * xx * x * x * x * x * x * x

?43 xx

Page 4: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Property: Multiply Powers with the Same Base

RULE:

the basesbases MUSTMUST be the same

baba xxx

Page 5: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Products of powers with the same base can be found by writing each power as a repeated multiplication.

Notice the relationship between the exponents in the factors and the exponents in the product 5 + 2 = 7.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 6: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

A.

Since the powers have the same base, keep the base and add the exponents.

B.

Group powers with the same base together.

Add the exponents of powers with the same base.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 7: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

C.

D.

1

Group powers with the same base together.

Add the exponents of powers with the same base.

Group the positive exponents and add since they have the same base

Add the like bases.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 8: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

A number or variable written without an exponent actually has an exponent of 1.

Remember!

10 = 101

y = y1

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 9: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

a. Simplify.

Since the powers have the same base, keep the base and add the exponents.

b.

Group powers with the same base together.

Add the exponents of powers with the same base.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 10: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

c.

Group powers with the same base together.

Add.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 11: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

d.

Group the first two and second two terms.

Divide the first group and add the second group.

Multiply.

8.3 – Multiplying Exponents8.3 – Multiplying Exponents

Page 12: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

8.3 – Multiplying Exponents

Examples:

a.

b.

c.

43 77

214 444

86 66

Page 13: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

8.3 – Multiplying Exponents

Multiplying powers in algebraic expressionsMultiplying powers in algebraic expressionsWhen multiplying, only combine the

things that are similar.Example:

you can rewrite it as

or

43 52 xx 4352 xx

710x

Page 14: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

8.3 – Multiplying Exponents

Try:

682 qq 435 936 xyx

Page 15: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Lesson #8.4Properties for Multiplying Exponents

Objective: SWBAT raise a power to a power and raise a product to a power.

Concept: Unit 8

Page 16: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

To find a power of a power, you can use the meaning of exponents.

Notice the relationship between the exponents in the original power and the exponent in the final power:

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 17: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 18: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Power Property.

Simplify.

1

Use the Power of a Power Property.

Zero multiplied by any number is zero

Any number raised to the zero power is 1.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 19: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Power Property.

Simplify the exponent of the first term.

Since the powers have the same base, add the exponents.

Write with a positive exponent.

C.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 20: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Power Property.

Simplify.

1

Use the Power of a Power Property.

Zero multiplied by any number is zero.

Any number raised to the zero power is 1.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 21: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Power Property.

Simplify the exponents of the two terms.

Since the powers have the same base, add the exponents.

c.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 22: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Powers of products can be found by using the meaning of an exponent.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 23: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Product Property.

Simplify.

Use the Power of a Product Property.

Simplify.

A.

B.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 24: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Product Property.

Use the Power of a Product Property.

Simplify.

C.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 25: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Product Property.

Simplify.

Use the Power of a Product Property.

Use the Power of a Product Property.

Simplify.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 26: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

Use the Power of a Product Property.

Use the Power of a Product Property.

Combine like terms.

Write with a positive exponent.

c.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 27: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

Simplify.

1. 32• 34

3.

5.

7.

2.

4.

6.

(x3)2

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents

Page 28: 8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 2 2 2. x x x x 3. Write each expression without using an exponent. 4.

7. The islands of Samoa have an approximate area of 2.9 103 square kilometers. The area of Texas is about 2.3 102 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.

8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents


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