1. OBJECTIVE:
The students will simplify expressions by using the 7 laws of exponents.

2. What do we want to know. How to write expressions using exponents
What do we want to know? *How to write expressions using exponents. *How to Multiply & Divide Powers *How to simplify expressions *How to evaluate algebraic expressions What should we understand? *Understand that exponents can be used to write expressions. *Understand that evaluating expressions may mean to SOLVE the expression. *Understand that multiplying exponents means to add the exponents AND dividing exponents means to subtract exponents. *Understand that the division rule is used to SIMPLIFY expressions. What should we be able to do? *Write expressions using exponents. *Evaluate/Solve expressions using exponents *Multiply & Divide Exponents *Simplify Expressions

3. All these things are described using exponents!

4. An exponent is simply shorthand for multiplying that number of identical factors.

5. So 4³ is the same as (4)(4)(4), three identical factors of 4.
x³ is just three factors of x, (x)(x)(x).

6. Exponent is the power in an expression.
13 7
Exponent
BASE

7. Using the Calculator
5 4
Press 5
Press ^
Press 4
Then =

8. 7 Laws of Exponents #1 PRODUCT LAW
To Multiply LIKE Bases…
…Copy the Base, Add Exponents

9. Product Law or Product Rule
YOU TRY:
52 ● 56 =??

10. 7 Laws of Exponents #2 QUOTIENT LAW
To Divide LIKE Bases…
…Subtract Exponents a4

11. Quotient Law or Quotient Rule:
YOU TRY:
87 = ???? 82

12. 7 Laws of Exponents #3 EXPONENT of EXPONENT LAW
To Raise a Power to a Power…
…Multiply Exponents
a12

13. Exponent of Exponent Law or Exponential Rule:
YOU TRY:
(62)5 = ???

14. 7 Laws of Exponents #4 Raising a product to a power
To Raise a QUANTITY to a Power, raise EACH Factor to that Power.
(-3ab)2= 9a2b2

15. 16a2b2 Exponent of Exponent Law or Exponential Rule:
EXAMPLE: (-4ab)2 =
(-4)2 (a)2 (b)2
(-4 ●-4), (a ● a), (b ● b) =
Note: If you don’t see an exponent…What exponent is actually there?
16a2b2
YOU TRY:
(5a2b) 2 = (5 ● 5), (a2 ● a2), (b ● b) =??

16. Exponent of Exponent Law or Exponential Rule:
(5a2b) 2 = (5 ● 5), (a2 ● a2), (b ● b) =??
25a4b2

17. 7 Laws of Exponents #5 Raising a quotient or a fraction to a power
To Raise a FRACTION to a Power, raise BOTH Numerator & Denominator to that power. a4 b4

18. YOU TRY:
(6) 5
(8) = ???

19. Stations:
Writing Expressions & Evaluating Expressions
Multiplying Powers
Divide Powers
Simplify Expressions
Evaluate Algebraic Expressions
Negative Exponents
Inequalities
Choose 6 out of 8
EARLY FINISHERS:
Make a test for your peers for a skill that we learned this week.
Multiple Choice
Fill in the blank
Essay (Explain)
That Quiz Modules

20. What do we want to know. How to write expressions using exponents
What do we want to know? *How to write expressions using exponents. *How to Multiply & Divide Powers *How to simplify expressions *How to evaluate algebraic expressions What should we understand? *Understand that exponents can be used to write expressions. *Understand that evaluating expressions may mean to SOLVE the expression. *Understand that multiplying exponents means to add the exponents AND dividing exponents means to subtract exponents. *Understand that the division rule is used to SIMPLIFY expressions. What should we be able to do? *Write expressions using exponents. *Evaluate/Solve expressions using exponents *Multiply & Divide Exponents *Simplify Expressions

21. 7 Laws of Exponents #6 NEGATIVE EXPONENT LAW
Negative Exponents 
…Reciprocal with a Positive Exponent 1
___ a3

22. #6: Negative Law of Exponents: If the base is powered by the
negative exponent, then the base becomes reciprocal with the
positive exponent.

23. Any nonzero number raised to the ZERO Power = ONE
7 Laws of Exponents #7
Any nonzero number raised to the ZERO Power = ONE 1 1 1

24. YOU TRY: 1000 = ? 15, 2380 = ? 0.5460= ? The Laws of Exponents:
#7: Zero Law of Exponents: Any base powered by zero exponent
equals one
YOU TRY:
1000 = ?
15, 2380 = ?
0.5460= ?

25. Let’s Review all 7 Laws…