Bellwork~ Simplify 1.) x • x3 2.) 53 • 55 3.) (32)3 4.) (-3x3y2)3 2.) 58 3.) 36 =1029 4.) -27x9y6 5.) 9x2 6.) -3x2

Bellwork~ Simplify Finish Worksheet 8.1 (1-24)

Today’s Objective To be able to apply the exponent rules when the exponent is negative or zero.

Exponent Rules 1.) am • an = 2.) (am)n = 3.) (a • b)m 4.) a-n = 3.) am • bm 4.) 1/an 5.) 1

A Table of 2’s 24= 23= 22= 21= 20= 16 8 4 2 2-1= 2-2= 2-3= 2-4= 2-5= Apply the Rule Describe the pattern 24= 23= 22= 21= 20= 16 8 4 2 2-1= 2-2= 2-3= 2-4= 2-5= 1/21= 1/22= 1/23= 1/24= 1/25= 1/2 1/4 1/8 1/16 1/32 1

Find the Pattern Notice the pattern and complete the table.

Negative Exponent 24= 23= 22= 21= 20= 16 8 4 2 1 2-1= 2-2= 2-3= 2-4= Let’s Look at the table of 2’s 24= 23= 22= 21= 20= 16 8 4 2 1 2-1= 2-2= 2-3= 2-4= 2-5= 1/21= 1/22= 1/23= 1/24= 1/25= 1/2 1/4 1/8 1/16 1/32

What’s the least number of times that you can go to McDonald’s? Negative Exponent What’s the least number of times that you can go to McDonald’s?

Is it possible to go to McDonald’s -1 times? Negative Exponent Is it possible to go to McDonald’s -1 times? NO If we can’t go to McDonalds -1 times, How can we express 2-1 ?

Negative Exponent 22 Means… 2 • 2 = So….. 21 Means… 2 = So….. What does 2-1 Mean?

Negative Exponent What does 2-1 Mean? You cannot leave an exponent negative because there is no way to express it’s meaning. 2-1 = 1/21 = 1/2

In order to maintain the pattern, 2-1 = 1/21 = 1/2 2-1= 2-2= 2-3= 2-4= 2-5= 1/21= 1/22= 1/23= 1/24= 1/25= 1/2 1/4 1/8 1/16 1/32

Negative Exponent Examples 1.) 3-2 = 2.) x-3 = 3.) xy-2 = 4.) (xy)-2 = 5.) (23)-2 = 1.) 1/32=1/9 2.) 1/x3 3.) x/y2 4.) 1/(xy)2 = 5.) Next Slide

Negative Exponent 5.) (23)-2 = Rule #2 2-6 = 1/26 = 1/64 Rule # 4 1/(23)2 = 1/26 = 1/64

You Try These 1.) 4-2 = 2.) y-2 = 3.) x2y-3 = 4.) (4-1)2 = 5.) 1/4-2 = 1.) 1/42=1/16 2.) 1/y2 3.) x2/y3 4.) 1/42 =1/16 5.) 42 = 16

Zero Exponent Let’s examine: 32 • 3-2 = 1.) 32 • 1/32 = 9 • 1/9 = 1 Now Try Rule #1 2.) 32 + -2 = 30 = 1 So….. Anything0 = 1

Zero Exponent Let’s Examine 72/72 72 = 7 • 7 So….. 72/72 = 7•7 = 1 7•7 Or…. 72/72 = 49/49 = 1 Or….

Zero Exponent If we apply Rule #6 to: Rule #6 72/72 = 72-2 = 70 = 1

Zero Exponent 1.) 170 = 2.) (5x)0 = 3.)(4x)0y-3 = 4.) 70 •2-2 = 5.) x-2 • x2 = 1.) 1 2.) 1 3.) 1/y3 4.) 1/4 = 5.) 1

Bellwork~ Simplify 1.) x • x-3 2.) 5-3 • 55 3.) (2-2)3 4.) (-3x3y2)3 2.) 52 3.) 1/26 4.) -27x9y6 5.) 9x2 6.) -x2/3

Today’s Objective To be able to apply the exponent rules when when dividing exponents with like bases.

Exponent Rules 6.) am an 7.) a n b 6.) am-n 7.) an bn

What’s the meaning of... But what about x5 x3

x2 x5 means x • x • x • x • x x3 means x • x • x So…. What’s the meaning of... x5 means x • x • x • x • x x3 means x • x • x So…. x5 = x • x • x • x • x x3 = x • x • x x2

What’s the meaning of... Explain the exponent rule for dividing with like bases to your `neighbor.

1.) x3 x5 2.) x3 x3 3.) x-3 What’s the meaning of... x3 = 1 x5 x2

The Secret ex.#1 Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer. For Example: x3 x5 Since x5 is on the bottom, the exponent will remain on the bottom in the answer 1/x2 .

The Secret ex.#2 Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer. For Example: x3 x-5 Since x3 is on the top, the exponent will remain on the top in the answer x8 .

The Secret ex.#3 Where ever the largest positive exponent is located in the problem is where the exponent will be in the answer. For Example: x-3 x-5 Since x-3/x-5 = x5/x3 and x5 is on the top, the exponent will remain on the top in the answer x2 .

Slates 1.) 43 • 42 = 1.) 45 2.) x6 2.) x2 • x4 = 3.) 8x3 3.) (2x)3 = 4.) 2-3 • 2-2 = 4.) 1/25 5.) 3x-5 = 5.) 3/x5

Slates 6.) 1/7x-2 = 6.) x2/7 7.) 8x-3• 1/y-4 8.) 49 8.) 76/74 = 7.) 8y4/x3 7.) 8x-3• 1/y-4 8.) 49 8.) 76/74 = 9.) (4/5)2 = 9.) 16/25 10.) (4/5)-2 = 10.)25 /16

Do the special problems worksheet

Classwork Do worksheets 8.2-8.3 homework page 409 (2-40 even)

Bellwork Simplify 1.) 4xy3 5xy-3 2y x2 2.) 14x3y -2xy -4xy-3 -x 3.) -9x3y7 (2xy)2 x2y3 -6x2y2

Bellwork Simplify 1.) 4xy3 5xy-3 2y x2 20x2 2x2y 10 y

Bellwork Simplify 2.) 14x3y -2xy -4xy-3 -x -28x4y2 4x2y-3 -7x2y5

Bellwork Simplify = 6xy4 3.) -9x3y7 (2xy)2 x2y3 -6x2y2

Then complete the Special Problems worksheet. Classwork Then complete the Special Problems worksheet. Homework Pg 426 (5-22)

Special Problems 1.) (8x3)2(¼x2)3 = 82x6 • 1/64x6 x12

Bellwork Simplify 3.) -18x3y3 -9xy5 2x2 y2

Bellwork Simplify 4.) 8x2y-2 (4xy2)-1 x-2y x2y 8x2 • x2 1 y2 • y (4xy2)x2y 8x4 4x3y6 = 2x y6

Bellwork Simplify 5.) 32xy3 -2xy -8x3y -4y -4y2 1x x2 2 -2y2 x

Bellwork Simplify 6.) 5x3y-1 (5x2y)-1 x-2y2 xy-1 5x5 y y3 (5x2y)•x

Classwork Do worksheets 8.3 homework page 425 (1-24) Quiz Monday Test Wednesday

Zero Exponent