Name
LESSON
7-3
Date
Class
Practice B
Multiplication Properties of Exponents
Simplify.
4
2
1. 3 · 3
2. 2 5 · 2 4
3 6 or 729
3. 2 3 · 2 5 · 2 1
2 9 or 512
4. q 6 · q 1
5. r 3 · r 4 · s 4
1
___
q
2 9 or 512
6. j 2 · j 4 · j 2
1
__
r
___
7
s
j4
4
9. g 4 5
8. h 2 7. c 5 · b 2 · c 3
2
8
1
___
c
___
b
2
h
0
10. w 6 10
g
12. (w 5) 2 · w 3
11. (v 2) 5 · v 4
1
v
1
____
14
w 13
3
2
14. a 2 · a 5 4
3
13. f 6 · f 2 1
___
15. 3b 4
81b 4
a 16
f 18
16. 5k 2
8
18. 3p 2
17. 4m 3
1
____
25k
2
⫺64m
3
9p 2
2
1
4
2
20. a 2 b 4 · a 2 b 3 · a 4 21. x 3 y 2 · x 2 y 3 3
2
19. s 4 t · s 4 t 3 1
______
s
20
t
9
a
10
b
5
x 16 y 2
22. The pitch of a sound is determined by the number of
vibrations produced per second. The note “middle C”
2
produces 2.62 10 vibrations per second. If a pianist
1
plays middle C for 5 10 seconds, how many vibrations
will occur?
2
1.31 ⫻ 10 or 131 vibrations
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c07-3_pr.indd 20
20
Holt Algebra 1
12/26/05 7:44:50 AM
Process Black
*À>V̈ViÊ
-ULTIPLICATION0ROPERTIESOF%XPONENTS
--"
LJÎ
LJÎ
#OMPLETEEACHEQUATIONTOSHOWTHEPROPERTY
AÊMÊÊN
AMqAN
AÊMN
M N
SA D 3IMPLIFY
AÊNÊÊBÊN
N
SABD q
3IMPLIFY
x
£Î
X qX Î x
X
A
qB qB N qN qN AÊÓÊB
Ê Ê{Ê
Ó
X
Î q { £Ó
ªND { { N nÊ£NÊ Ê
q
£Ó
SB D qSB D qB £x
BÊ Ê
È
£Ó
œÌʏ}iLÀ>Ê£
OR
n£ÊBÊ{Ê
SPD Î
È{ÊMÊ Ê
ÚÚÚÚ
Ê £Ê ÊÊ
™ÊPÊÓÊ
SAB
D qSAB
D qA SXY D qSXY D SÊÓäÊÊTÊ
AÊ£äÊB
Ê ÊxÊ
ÚÚÚÚÚÚ
Ê £Ê ÊÊ
ÊXÊ£ÈÊÊYÊÓÊ
£°Î£ÊÊ£ÊäÊÓʜÀʣΣÊۈLÀ>̈œ˜Ã
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
œÌʏ}iLÀ>Ê£
,iÌi>V…
-ULTIPLICATION0ROPERTIESOF%XPONENTS
LJÎ
OR
X T OR
MN
GH
D ???
A
???
S R S D
T T
-OSTSTATESAREIRREGULARLYSHAPED(OWEVERTHESHAPES
OFSOMEWESTERNSTATESAPPROXIMATERECTANGLES
7YOMINGISNEARLYRECTANGULARWITHAWIDTHOFABOUT
FEETANDALENGTHOFABOUTFEET
7HATISTHEAPPROXIMATEAREAOF7YOMING
7RITEYOURANSWERINSCIENTIFICNOTATION
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
A B J ???
K 3IMPLIFYTXE Y
S D X Y
2
3 2
X Y
8 2 5 3 8 6
SHD
3
4
2 2 B 3IMPLIFY
SJK D qSJD &INDTHEMISSINGEXPONENTINEACHEXPRESSION
B qB B Y SD
A
n
???
X
A
B
3IMPLIFYT E J K 4 3 5
Sa mD a mn ApMANDNAREINTEGERS
SRS D qSRS D ?????
XY
SXY D qSXY D SAB
D qSAB
D B C
9OUCANUSETHE0OWEROFA0OWER0ROPERTYTOFINDAPOWERRAISEDTOANOTHERPOWER
S DS D
SJ K D 3IMPLIFYa 4 b 5 a 2
X SXYD qSYD
SDDqD
Y SBCD ???
a m a n a m nApMANDNAREINTEGERS
3IMPLIFYT ET E #OUNTTHENUMBEROFFACTORS
4HENUMBEROFFACTORSISTHEEXPONENT
/RYOUCANUSETHE0RODUCTOF0OWERS0ROPERTY
SXD SGHD S T %XPANDEACHFACTOR
XY
YqX qSY D qSX D SYD M qSN D qN SMD S4 4 4 DS4 4 4 4 4 D
S qS qT SD OR
S DS D
X qX ??
3IMPLIFYT ET E
q T qT AK4up.indd 71
SBD AÊ£ÈÊ
ÓxÊKÊÓÊ
,%33/.
q £Î
ÊWÊ Ê
9OUCANMULTIPLYAPOWERBYAPOWERBYEXPANDINGEACHFACTOR
q
SMD 3IMPLIFY
ÚÚÚÚ
Ê £Ê ÊÊ
4HEPITCHOFASOUNDISDETERMINEDBYTHENUMBEROF
VIBRATIONSPRODUCEDPERSECOND4HENOTEhMIDDLE#v
PRODUCESVIBRATIONSPERSECOND)FAPIANIST
PLAYSMIDDLE#FORSECONDSHOWMANYVIBRATIONS
WILLOCCUR
*À>V̈ViÊ
-ULTIPLICATION0ROPERTIESOF%XPONENTS
ÚÚÚ
Ê ££ÈÊ ÊÊ
ÊCÊ Ê
È{ÊAÊ ÊBÊ Ê
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
ÊGÊ Ê
W qW VÊ£{Ê
SSTD qSSTD 4HEVOLUMEOFACUBECANBEFOUNDBYUSINGTHEFORMULA
6SWHERESREPRESENTSTHELENGTHOFEACHSIDEOFTHE
CUBE&INDTHEVOLUMEOFACUBEIFEACHSIDEISAB
SA D qSA D ÊFÊ Ê
ÚÚÚ
Ê £nÊÊÊ
HÊ£äÊ
ÚÚÚ
Ê ££nÊ ÊÊ
Î
£
SKD SC D qSC D JÊÊ{Ê
SA D qA ÚÚ
Ê£ÊÊ
£
T
SG D SF D qSF D T
qT £Ó T qT nÊXÊ Ê
ÊSÊ Ê
V qV {
ÚÚÚ
R{ ÊÊ
ÊBÊ Ê
S D T qT Î
CÊ ÊÊ
ÚÚÚ
Ó
£
?????
Î
ÊÓÊ ÊœÀÊx£Ó
J qJ qJ n
B SXD Î Î X {
™
SH D SW D SBD Ó q {
B
BÊnÊ
ÊQÊ Ê
n
R ÊÓÊS
Ê ÊxÊ
£
ÊÓÊ ÊœÀÊx£Ó
C qB qC q q ™
R qR qS £ÊÊÊ
ÊÚÚÚ
Ç
S D
äqx
ä
S D LJÎ
ÊÎÊ ÊœÀÊÇә
Q qQ R qS qR N
q È
q Ó Ç
q x n
,%33/.
*À>V̈ViÊ
-ULTIPLICATION0ROPERTIESOF%XPONENTS
--"
MN
S5
SQUAREFEET
(OLT!LGEBRA
3
3
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
71
2
S4 3D 4
X Y 4
2
5
3
Su D Sv D ?????
???
2
3
Sx D y 2
S6 4D D 4 0
???
m 8 n 4 m 7
???
H 2 4 3 5 2 8 3 2
????
V U
(OLT!LGEBRA
Holt Algebra 1
5/26/06 10:50:03 AM