Do Now

Solve each equation in your lecture notebook. Write out your steps!!!!! Without talking!!!!!

1) 3( z + 7) =123

2) 1/3(x – 6) = 6

3) 5y – 3y + 4 = 3y + 8

4) 6g – 5 = 7g + 7

Exponent Rules

Objective

Students will be able to: 1) demonstrate their understanding of exponent rules and 2) solving word problems by correctly solving 2 exponent rule problems and 2 word problems at a basic level of proficiency.

2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

California Standards

Definition of Exponent An exponent tells how many times a

number is multiplied by itself.

34

BaseExponent

34= 3 x 3 x 3 x 3

Multiplying with Exponents Rule: When multiplying like bases, add

the exponents. So and

m n m na a a

52 123 175f f f71 3

8 842 3 6w w w

3 5 5 3 5 1 5 8 63 4 12 12y z y z y z y z

Multiplying Exponents

nm mna aRule:

53 3 3 3 3 3 3 5 15x x x x x x x x

Notice there is only one base.

An easier way would be to multiply the 3 and 5 to get the new exponent

of 15.

Dividing with Exponents

Rule:

When dividing like bases, subtract the exponents.

mm n

n

aa

a

543543 215 328

215

kk k

k

259

16

12 3

20 5

ss

s

52

3 1

r rrrrr rrrrr rrr

r rrr rrr

Negative Exponents

Notice what happens with the example 3

3 6 3

6 3

1 1h hhhh h

h hhhhhh hhh h

This leads to another rule.

Rule:

1 1 and n n

n na a

a a

When the Power is Zero

Rule: Anything to the zero power is 1.

0 1a

33 3 0

3

xx x

x or all cancel for

an answer of 1.

ExamplesSimplify each expression.

34 88)1 52)2 yyy 25323 ))()(3 baba

5

24

4)4

24)7 6

2)5x

x7

52

5

)6qp

qp

3)8 m 1)9 ab 0)10 p

You trySimplify each expression.

42 55)1 523)2 yyy 2642 ))()(3 nmmn

6

27

7)4

22)7 7

2)5a

a3

22

4

)6yx

yx

4)8 y 23)9 c 03)10

Solving Word Problems

“Word Problems scare me!”

“Word Problems make me nervous!”

“Word Problems?

I just skip them!”

Not anymore!!!!!!!Here are the steps:

Step 1 – Panic: ok; don’t quit.Step 2 – Identify the problem.Step 3 – Organize the givens .Step 4 – Connect.Step 5- Solve .

Ex 1: The length of a rectangle is 6 in. more than its width. The perimeter of the rectangle is 24 in. What is the length of the rectangle?

Ex 2: Half a number plus 5 is 11. What is the number?

Ex 3: The sum of three consecutive integers is 147. Find the integers.

You try: The sum of three consecutive integers is 48. Find the integers.

You try: A customer pays 50 dollars for a coffee maker after a discount of 20 dollars. What is the original price of the coffee maker?

You try: The dance club sold 200 concert tickets and collected $640. A student ticket cost $2 and an adult ticket cost $5. How many of each type of ticket were sold?

Exit Ticket

3) Carol collects car models. She buys 3 Camaro models that cost $23.50 each and 2 Mustang models. She spends a total of $110 on all the models. How much does each Mustang model cost?4) Allen was looking over his finances and found that in 5 visits to Outback, he spent $52 on steak tacos. This amount includes $17 in tips. How much did each steak taco cost before the tip?

23462 ))()(1 baba

3

2

3

4

4)2

x

x