Exponents
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Name
Exponents
P t-2
Write each power as a product and then evaluate.
1. 32
2.
g3
3.
53
4.
103
5.
35
6.
4 squared
7. Reasoning
ls 4
x
2 equal to 42? Explain why or why not.
Write each product in exponential form.
8.
9. 12x12x12x12
35 squared
10. 28 x 28 x 28 x 28 x
28
11. 22 cubed
12. Some computer virus programs are based on exponents. A
certain program could begin with 4 screens. When it has been
cubed, how many screens will be affected?
13. Write 2 x 2 x 2 x 2 x 2in exponential form and as
a product in standard form.
Test Prep
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14. Which shows 5 squared in exponential form?
A.'10
8.25
C.52
15. Writing in Math Zach began with $10 in investments and was
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c
D.5x5
able to "triple" his money. Alli also began with $10. She was able
to "cube" her money. Who ended up with more money? Explain.
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Name
Exponents
base
---J
35
R 1-2
<---
exponent
How to write a power as a product
and then evaluate:
The number 3 is the base.
It is the factor that is multiplied.
24
The number 5 is the exponent.
It tells how many times the base is used
The base (2) is used as a factor
the number of times as shown by
35 is read "three to
35
:
a.s a factor.
the exponent (4):
ihe fifth power.,,
3x3x3X3x
g-)Five
2a:2x2x2x2:16
factors of 3
are multiplied.
How to write a product in
exponential form:
How to use exponents to write a number in
expanded torm:
5X5X5
Step 1: Write the base.
:
5
Step
2:
(4
x 103) + (5 x
j02) + (1
x
101)
+ (2 x
1Oo)
Count the number of
times the base is used
as a factor. This is the
exponent.
53
Write each power as a product and then evaluate.
1.
53
2.
25
3.
73
Write each product in exponential form.
4.8x 8x8
5,20.20.20.20
(0
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c
Write the number in expanded form using exponents.
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6. 1,324:(1 x103) +(3x10r)
7. Number sense
2
Use with Lesson 1-2.
Are
*(--___)+(
2a and 42 equar? Exprain why or why not.
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Name
Exponents
1'
The Moon is 2.3g
standard form.
PS t"2
x
10s mi from Eadh. write the distance
in
2. Pluto is 3,647,200,000 mi from the sr.rn. write the
Pluto is from the Sun in expanded form,
distance that
,.ing Liptn"ntr.
3. A
lew,com.puter program hits the market, and for g days its
sales doubre each day. rf onry one program
sord the first day,
how many will sell on the ninifr Oay?
4. The yellow buckeye tree has reaves
that are made up of five
leaflets. lf there aie five twigs on Lrun"h
that have five reaves
on each twig, how many teifrets are
" on the branch?
write your
answer in exponentiarform and in standard
form.
5.
To find the vorume of a cube, take
the renEth of a side to the
what is the vorume of a cube'tr'"i r,as side
rength
*'ixH.ry"r.
6'
"
Writing in Math Write one million as a power
of ten. Write one
billion as a power of ten. A googor is 1d1oo.
H* i-,"ny zeros are
in the standard form of on"
fooiol? Explain.
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2
Use with Lesson 1-2.
Name
Power Patterns
E 1.2
PATTERNS
21
:
22:
23:
24:
25:
n6
z:
27:
01
:
51
32:
33:
34:
35:
36:
37:
=
52=
13-
54:
55:
c6-
57:
aBr,
a9u
1' complete the Powers of 2 column in the
chart.
2'
Then, describe the pattern you
see.
complete the Powers o/3 column in
the chart. Then describe the pattern
you see.
3' How are the patterns for powers of 2 and powers
of 3 the same?
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?;ff:H;1",#lfJiil:i:xpect
to rind in the powersors corumn
in the chart.
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o@
2
Use with Lesson 1-2.
a
Write each power as a
t-
poduct and then evaluate
2.
3r
4.
103
6. 4squaed
3s
7. Reasoning
ls 4
x
x
Ttu nunber 3ls hs
bftrihal
h is
lho
Th6
nuhhr
It
blls
33 is rcad
35
= 3 x
tEe b he
3x
3 x
andlhen €€lualel
@.
is muliplisd.
5 is h€ sxpBnt
mary lim6s h baso is
iil
nfrh
as a
ladd
lftrl
21=2x2x2\2=16
3x 3+FVabdoEdg
a
prdd
in
How to
dpnonllslbm:
2 meale 4 is
lador
he numberotlimesasshown by
The base (2) is used as a
usd
ars munipbd-
H@ to srh6
2 equal to 42? Explaih why or why not
Ho. 6ample answen 4
bss+36+exponsil
83
8xBx8:512
3x&0
5 x 5 x 5;125 lo_alQ_xlollJ(to
S x_Q rl t<_0_X3?49 4 x 4; t6
5.
R 1.2
Exponents
Exponents
u$
exponenb ro wde a numbef rn
4,512 = (4
x
1,000) + {5
= (a
x
103) + (5
Sl€pl: Wdblhobse.
x
x
+0 x
100)
101 + (1
x
10) + (2
101)
+
(2
x
x
1)
109
5
Sbp2: Countlhenum&rol
8.
35 squared
10.2A x2A
x28x28\28
lh€s lhs
9.12x12x12X12
11. 22 ctbed
tr
14
E
t" y;::ffi'"#;"ilil.exponentiarromanda" 25: s2
t.
53
2.
25
g.
73
B.zs
10
2 usewilhksent
D.5X5
05'
6. 1,324=(1
31-2
PANEBXS
2'=
23=8
.'= 81
"r:18
," =92
""=2&
""=7N
t'=21187
=&
"':128
""=2#
2" -512
'"=6,561
.":19,68{l
21a=I it A
3,": EiO llto
=5
u'=25
2.
=126
*n
r-,
mi frcm Eanh. Write the distance in
mi
fom the Sun. Write fre distance that
=6?3
s" =
19,G25
u'=781128
u"
-
u"=
A new computer pogram hits the market, and for I days its
sales double each day. lf 6ry one progEm sold the firet day,
how many will sell on the ninth day?
300,625
1,953,125
256 nroorams
s1a=6t,!.EAltE
Tho yellow buck€y€ tr€€ has leav6 that are made up of five
leallets. lf there a€ five lwigs on a branch that have five leaves
on €ach hillg, how many l€aflets are on the branch? Writ6 your
answer in exponential fom and in stdddd form.
se
of2 column in the cxd. Then. describe the oanem vou
12$laaflatc
532
p
To find the volume
Complete the powe6 ol 3 column in the chart. Then describe the pattem you
ol a cube, take the length of a side to the
third power What is the volume ot a cube that has a sid6 length
of 12 in.?
s$.
T
1-t281ns
product triples.
3.
How are the patterns for powers ot 2 and pow€c of 3 the
w'ftlng in M6th Wdte on6 million 6 a power of ten. Wdte ono
billion 6 a powerotlen. A googol is 10100. How many zercs ar6
in the stffdard fm ol on€ googol? Explain.
sme?
Samole an$wer: ld: l0e: Thate are
l0O zeros ln a oooool. Tha oower a{
ten is always tlre same as the number
of :eros aftor tho whole number baee.
T
p
4.
Describe the patem you expect to find in ths Powers ol 5 column ln tho chart.
Then, complgte the chan.
T
product will lncrease fi
2
1O5
Pluto is 3,647,200,000 mi
T
2.
2
x
The Moon is 2.39
"u"=31125
anawers sivon tor 1-4.
Complete
u**nn
23O.O0O
51
'"
ld)
42 equal2 Explain why or why not.
standad fom.
PowGB ol 5
3'=g
3'=9
," =27
4
ed
X !
