Properties of integer exponents edmodo 2012 13

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

Properties of Integer Exponents



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

85353 222 2

Multiplication Property


63 63+565

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

Add the Exponents



b7 b5 = b 12pull to the right for answer

f 2 h4

What can I do with this?

= ?



r3r8 r-5 =Erase here for answer

238 23-5 = 233



It's your turn

c2 c5 = c7move for answer




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!


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

n

m

aa

a


2353

5

22 2

2

Division Property


1

66

666

66666

Subtract the Exponents

Division Property

353

5

6 6

6 3662


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.


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


62323 222

Raising a Power to a Power


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


Simplest Form

• Each base appears exactly once

• There are no negative exponents

• There are no powers of powers



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


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


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


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


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


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

variables(2x2y3)(3xy-4)

4x4y6 ÷ 2x-2y8


Multiplying/Dividing with Integer Exponents

(2x2y3)(3xy-4)


Multiplying/Dividing with Integer Exponents

4x4y6 ÷ 2x-2y8

Documents

Properties of integer exponents edmodo 2012 13