1. Multiplying Powers
With The
Same Base

2. Rules of Exponents
Exponents give us many shortcuts for multiplying and dividing quickly.
Each of the key rules for exponents has an importance in algebra.

3. Rules of Exponents
25 = 2 • 2 • 2 • 2 • 2 = ?
We know 2 • 2 = 4
4 • 2 = 8
8 • 2 = 16
16 • 2 = 32
So 2 • 2 • 2 • 2 • 2 = 32

4. Rules of Exponents
An exponent tells how many times a number is multiplied by itself. 3 4
Exponent
Base
4•4•4
= 64

5. How do we write in exponential form?
Rules of Exponents
How do we write in exponential form?
Answer:

6. How do we write in exponential form?
Rules of Exponents
How do we write in exponential form?
Answer:
Notice:

7. = Write each in Exponential Form. 2 3 2 3 2 3 2 3 · · ·
Rules of Exponents
Write each in Exponential Form. 2 3 2 3 2 3 2 3 =

8. Write each in Factored Form.
Rules of Exponents
Write each in Factored Form.

9. Can you think of a quick way to come up with the solution?
Properties of Powers
If x3 means x • x • x
and x4 means x • x • x • x
then what is x3 • x4 ?
x • x • x • x • x • x • x
= x7
Can you think of a quick way to come up with the solution?

10. Your shortcut is called the Product of Powers Property.
Properties of Powers
Just Add the Exponents!
Your shortcut is called the
Product of Powers Property.

11. Product of Power Property
When multiplying powers with the
same base, just ADD the exponents.
For all positive integers m and n:
Ex: 3 4 4 2
3 + 2 4 4 5 = =
4 4 4 5 =

12. Product of Power Property
Try This One!
What is 31 • 34 • 35?
Since we are multiplying like bases just add the exponents.
Answer: 3( ) =
310

13. Product of Power Property
Simplify.

14. Product of Power Property
Simplify. 1

15. Product of Power Property
Simplify.

16. Power of a Power Property
(7b5)2
= 72(b5)2
(7b5)(7b5)
= 49b10
(5x3)2
= 52(x3)2
(5x3)(5x3)
= 25x6
Can you think of a quick way to come up with the solution?

17. Just Multiply the Exponents!
Power of a Power Property
Just Multiply the Exponents!
Your short cut is called the
Power of a Power Property.

18. Just Multiply the Exponents!
Power of a Power Property
Just Multiply the Exponents!
(a2)3
= a2 • a2 • a2
= a2+2+2
= a6
Your short cut is called the
Power of Power Property.

19. Power of a Power Property
To find the power of a power, you MULTIPLY the
exponents. This is used when an exponent
is on the outside of parenthesis.
(51a2b)3
53a2•3b3
125a6b3

20. Power of a Power Property
To find the power of a power, you MULTIPLY the
exponents. This is used when an exponent
is on the outside of parenthesis.
(21x3)5
25x3•5
32x15

21. Power of a Power Property
6(31y5z)2
6(32y5•2z2)
6(9y5•2z2)
54y10z2

22. Simplify Using What You Just Learned
Multiplying Powers
Simplify Using What You Just Learned 2) 1)

23. Simplify Using What You Just Learned
Multiplying Powers
Simplify Using What You Just Learned 3) 4)

24. Simplify Using What You Just Learned
Multiplying Powers
Simplify Using What You Just Learned 6) 5)

25. Simplify Using What You Just Learned
Multiplying Powers
Simplify Using What You Just Learned 8) 7)

26. Take Out Your Study Guide!!!
Multiplying Powers
That's all Folks!
That’s all folks
Take Out Your Study Guide!!!

27. Negative Exponent on a Fraction
#10
Just flip the fraction over to make the exponent positive!

28. Product of Power Property
#11
Product of Power Property
When multiplying powers with the
same base, just ADD the exponents.
For all positive integers m and n:
am • an = am + n
Ex :
(32)(33) = (3 • 3) • (3 • 3 •3)
= = 35
(x5)(x4) = x = x9

29. Power of a Power Property
# 12
Power of a Power Property
To find the power of a power, you MULTIPLY the
exponents . This is used when an exponent
is on the outside of parenthesis.
= 125a6b3
= 53a2•3b3
(51a2b)3
(21x3)5
= 32x15
= 25x3•5
= 72y16z2
8(31y8z)2
= 8 (32y8•2z2)

30. Extra slides

31. Simplifying Expression
#11
Simplify.