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

2. 3x3 2x2x2x2x2x2 10x10x10 5x5x5 1x1x1x1x1x1x1x1 Write in
exponential form
3x3
2x2x2x2x2x2
10x10x10
5x5x5
1x1x1x1x1x1x1x1

3. HISTORY of the word EXPONENT.
The term EXPONENT was introduced by Michael Stifel ( ) in 1544 in Arithmetica integra.

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

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

7. Exponents
exponent
power
base

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

9. 7 Laws of Exponents #1 PRODUCT LAW
To Multiply LIKE Bases…
…Copy the Base, Add Exponents

10. Product Law or Product Rule

11. 7 Laws of Exponents #2 QUOTIENT LAW
To Divide LIKE Bases…
…Subtract Exponents a4

12. Quotient Law or Quotient Rule:

13. 7 Laws of Exponents #3 EXPONENT of EXPONENT LAW
To Raise a Power to a Power…
…Multiply Exponents
a12

14. Exponent of Exponent Law or Exponential Rule:

15. 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

16. 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. 7 Laws of Exponents #6 NEGATIVE EXPONENT LAW
Negative Exponents 
…Reciprocal with a Positive Exponent 1
___ a3

19. #6: Negative Law of Exponents: If the base is powered by the
negative exponent, then the base becomes reciprocal with the
positive exponent.

20. 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

21. The Laws of Exponents:
#7: Zero Law of Exponents: Any base powered by zero exponent
equals one

22. Basic Examples

23. Basic Examples