properties of integer exponents edmodo 2012 13

How do I simplify and evaluate algebraic expressions involving integer exponents?

Properties of Integer Exponents

How do I simplify and evaluate algebraic expressions involving integer exponents?

How do I simplify and evaluate algebraic expressions involving integer exponents?

• To multiply powers with the same base, keep the base and add the exponents nmnm aaa

85353 222 2

Multiplication Property

How do I simplify and evaluate algebraic expressions involving integer exponents?

63 63+565

)(6 6 6 6 6 6 6 6()68

Add the Exponents

Multiplication Property

How do I simplify and evaluate algebraic expressions involving integer exponents?

b7 b5 = b 12pull to the right for answer

f 2 h4

What can I do with this?

= ?

Multiplication Property

How do I simplify and evaluate algebraic expressions involving integer exponents?

r3r8 r-5 =Erase here for answer

238 23-5 = 233

Multiplication Property

How do I simplify and evaluate algebraic expressions involving integer exponents?

It's your turn

c2 c5 = c7move for answer

Multiplication Property

How do I simplify and evaluate algebraic expressions involving integer exponents?

Multiplication Property

d6 d-9 ==

=

1.

72 782.

d-3

710

16 16-83. 16-7

move for answer

move for answer

move for answer

It's your turn!

How do I simplify and evaluate algebraic expressions involving integer exponents?

• To divide powers with the same base, keep the base and subtract the exponentsnm

n

m

aa

a

How do I simplify and evaluate algebraic expressions involving integer exponents?

2353

5

22 2

2

Division Property

How do I simplify and evaluate algebraic expressions involving integer exponents?

1

66

666

66666

Subtract the Exponents

Division Property

353

5

6 6

6 3662

How do I simplify and evaluate algebraic expressions involving integer exponents?

Division Property

23

5

22

2

88

3

5

2

12

2

2

8

3

5

22

2 2

23

5

2

12

2

2

25

3

22

2

22

5

3

2

12

2

2

It's your turn!

2.

1. 3.

4.

5.

6.

How do I simplify and evaluate algebraic expressions involving integer exponents?

• To raise a power to a power, keep the base and multiply the exponents nmnm aa

How do I simplify and evaluate algebraic expressions involving integer exponents?

62323 222

Raising a Power to a Power

How do I simplify and evaluate algebraic expressions involving integer exponents?

1

821

(84)6 = 84 6 = 824

(83)-7 = 83 -7

=(4-4)-5 4-4 -5

Raising a Power to a Power

=

= 8-21 =

420

How do I simplify and evaluate algebraic expressions involving integer exponents?

Simplest Form

• Each base appears exactly once

• There are no negative exponents

• There are no powers of powers

How do I simplify and evaluate algebraic expressions involving integer exponents?

How do I simplify and evaluate algebraic expressions involving integer exponents?

Adding Exponential Terms

• In order to add exponential terms, both the base and the exponent must be the same. Otherwise, they must be multiplied out before they can be added.

• 72 + 72 = 2 x 72 = 2 x 49 = 98

• x2 + x2 = 2x2

How do I simplify and evaluate algebraic expressions involving integer exponents?

Multiplying in Scientific Notation

• Multiply the coefficients• Use properties of exponents to

multiply the power of 10• Simplify

4 x 103 • 3 x 104

12 x 107

1.2 x 108

How do I simplify and evaluate algebraic expressions involving integer exponents?

Dividing in Scientific Notation

• Divide the coefficients• Use properties of exponents to

divide the power of 10• Simplify

2 x 107 ÷ 4 x 104

.5 x 103

5 x 102

How do I simplify and evaluate algebraic expressions involving integer exponents?

Practice1. 2 x 107 • 4 x 104

2. 5 x 10-6 • 4 x 10-3

3. 3 x 10-3 • 4 x 104

4. 8 x 106 ÷ 4 x 105

5. 6 x 103 ÷ 3 x 10-6

6. 9 x 10-5 ÷ 2 x 10-2

How do I simplify and evaluate algebraic expressions involving integer exponents?

POD 4 Sep

• Today, the United States National Debt (how much we owe) is projected to pass $16,000,000,000,000. The number of taxpaying citizens in the U.S. population is a little more than 100,000,000. If the debt is divided equally among all taxpaying citizens, how much does each taxpayer owe?

1. Represented in scientific notation

2. Represented in standard form

How do I simplify and evaluate algebraic expressions involving integer exponents?

Multiplying/Dividing with Integer Exponents• Multiply/Divide the coefficients• Use properties of exponents for the

variables(2x2y3)(3xy-4)

4x4y6 ÷ 2x-2y8

How do I simplify and evaluate algebraic expressions involving integer exponents?

Multiplying/Dividing with Integer Exponents

(2x2y3)(3xy-4)

How do I simplify and evaluate algebraic expressions involving integer exponents?

Multiplying/Dividing with Integer Exponents

4x4y6 ÷ 2x-2y8