Transcript Multiplication Property of Exponents

MULITIPLICATION
PROPERTIES OF
EXPONENTS
September 17, 2012
Exponent  the number of times the base
is used as a factor.
Base  the number or Variable that undergoes repeated
MULTIPLICATION .
2
4
EXPONENT
means
2  2  2  2  16
BASE
Basic Terminology
Important Examples
x 5 means (use parentheses for multiplica tion) ( x)( x)( x)( x)( x)
y 3 means ( y)( y )( y)
Variable Expressions
MULTIPLICATION
PROPERTIES
PRODUCT OF POWERS
This property is used to combine 2 or more exponential expressions with the SAME base.
2 2
3
3
5
4
( x )( x )
(2  2  2)(2  2  2  2  2)
( x)( x)( x) ( x)( x)( x)( x)
28
x7
256
I DO:
Multiplying Powers with the Same Base
Multiply. Write the product as one power.
A. 46 • 68
Add exponents.
B. k8 • k10
k 8 + 10
k 18
Add exponents.
WE DO :
Multiplying Powers with the Same Base
Multiply. Write the product as one power.
C. 76 • 7
76+1
77
Think: 7 = 7 1
Add exponents.
D. 189 • 1811
18 9 + 11
18 20
Add exponents.
YOU DO:
Multiply. Write the product as one power.
A. 35 • 32
35 + 2
37
Add exponents.
B. c22 • c11
Add exponents.
c 22 + 11
c 33
MULTIPLICATION
PROPERTIES
POWER TO A POWER
This property is used to write an exponential expression as a single power of the base.
(52 ) 3
(x 2 ) 4
(52 )(52 )(52 )
( x 2 )( x 2 )( x 2 )( x 2 )
56
x8
RAISING A POWER TO A POWER
Reading Math
4 5
(9 )
is read as “nine to the fourth, to the fifth.”
I DO: Raising a Power to a Power
Simplify.
A. (10-2)2
(10-2)2
= 10-2 • 2Multiply exponents.
= 10-4
B. (612)4
(612)4
= 612 • 4 Multiply exponents.
= 648
WE DO:
Simplify.
A. (311)4
(311)4
= 311 • 4 Multiply exponents.
= 344
B. (415)2
(415)2
= 415 • 2 Multiply exponents.
= 430
YOU DO:
Simplify.
A. (912)6
(912)6
= 912 • 6 Multiply exponents.
= 972
B. (11-4)2
(11-4)2
= 11-4 • 2Multiply exponents.
= 11-8
Power of a Product Property

To find a power of a product, find the
power of EACH factor and multiply.

I DO:
(4 yz )  4  y  z  64 y z
3
3
3
3
3 3
14
Practice Power of a
Product Property
1.
We DO:
2.
You Do: 6  3
(2mn)
 
8
6
2
 
4
2
(abc)
4
15
MULTIPLICATION
SUMMARY
PROPERTIES
PRODUCT OF POWERS
x x  x
a
b
a b
ADD THE EXPONENTS
POWER TO A POWER
MULTIPLY THE EXPONENTS
x 
a b
x
a b

Product of Powers Property—To multiply powers
that have the same base, ADD the exponents.

Power of a Power Property—To find a power of a
power, multiply the exponents.

Power of a Product Property—To find a power of a
product, find the power of each factor and
multiply.
Review Multiplication Properties
of Exponents
17
Place the numbers at in any spot on you
MATHO card.
 Be sure to show all your work for each
problem to get participation points.


1st Winner
2nd Winner
Exponent MATHO
3rd Winner
1. n3  n4
2. 8 • 88
3. (33)4
4. 33 • 32 • 35
5. 412 • 417
6. (172)
–20
7. x5 • y2
8. x2 • x3
9. (67)9
10. (134)
–10
11. 42 • 44
12. 25 • 2
13. (54)2
14. (9-8)9
15. 244 • 244
16. n5 • n7
17. (48)2
18. 86 • 83
19. 46 • 44 • 42
20. 66 • 63
21. 126 • 1210
22. (105)-6
23. 911 • 9-3
24. (108)6
25. 86 • 8-12