Download Exponents and Square Numbers

Name
Lesson 11.7
Exponents and Square Numbers
Write in exponent form. Then find the value.
1. 5 5 5
2. 2 2
3. 8 8 8 8
4. 4 4 4 4 4
Find the value.
5. 122
10. 83
6. 55
7. 73
8. 18
11. 46
12. 32
13. 113
9. 115
14 57
Compare. Write ,, ., or ⴝ.
15. 53
23
16. 22
41
17. 54
78
18. 62
93
Problem Solving and Test Prep
USE DATA For 19–20, use the pattern in the table.
19. James earned 729 pennies. How many
plates did James wash in all?
Pennies Earned
20. What number in exponent form
represents the number of pennies James
would earn for washing 11 plates? How
many pennies would he earn for washing
11 plates?
21. Which is greater than 92?
Number of plates
washed
Pennies
Exponent
form
Start
1
30
1
3
31
2
9
32
3
27
33
22. What is the greatest square number
that is even and is less than 300? What
is the value of this square number?
A 2
7
43
C 52
D 41
B
PW71
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L07.indd PW71
6/28/07 1:12:26 PM
Name
Lesson 11.7
53; 125
3. 8 8 8 8
22 ; 4
4. 4 4 4 4 4
45; 1,024
84; 4,096
6. 55
144
10. 83
7. 73
8. 18
13. 113
9
4,096
.
23
16. 22
2ⴛ2ⴛ
5ⴛ5
161,051
1
12. 32
2ⴛ2
14 57
1,331
78,125
Compare. Write ,, ., or ⴝ.
15. 53
Check
diagram.
41
17. 54
,
78
18. 62
,
5 ⴛ 31
3ⴛ7
Rewrite the prime factorization by using exponents.
6. 2 5 7 2
ⴝ
5. 21
9. 115
343
3,125
11. 46
512
prime factorization of 48. Write
the prime factorizaton.
Find the prime factorization. You may use a factor tree.
2. 4
3. 100
4. 155
Find the value.
5. 122
2ⴛ2
ⴛ2ⴛ
6
1. Draw a factor tree to find the
Write in exponent form. Then find the value.
2. 2 2
Lesson 11.8
Prime Factorization
Exponents and Square Numbers
1. 5 5 5
Name
7. 3 3 7 3 7
22 ⴛ 5 ⴛ 7
93
8. 19 19 19 19
3 3 ⴛ 72
194
Find the number for each prime factorization.
9. 3 73
Problem Solving and Test Prep
10. 5 5 5 3
1,029
USE DATA For 19–20, use the pattern in the table.
19. James earned 729 pennies. How many
13. 11 2 2
plates did James wash in all?
Pennies Earned
6 plates
20. What number in exponent form
represents the number of pennies James
would earn for washing 11 plates? How
many pennies would he earn for washing
11 plates?
14. 82 23
48
Number of plates
washed
Pennies
Exponent
form
Start
1
30
1
3
31
2
9
3
2
3
27
33
17. The prime factors of a number are the
factors of 36?
that is even and is less than 300? What
is the value of this square number?
B
number are 2, 7, and 3. Two is repeated
once. What is Patrick’s favorite number?
84
A
20. What is the least number that is the
product of two different primes that are
squared?
A 2 and 3
B
11 and 3
C
5 and 2
36
D 4 and 13
172; 289
Circled problems are suggested homework problems.
Circled problems are suggested homework problems.
Practice
PW71
250
18. The prime factors of Patrick’s favorite
first four prime numbers. No factor is
repeated. What is the number?
22. What is the greatest square number
43
C 52
D 41
16. 2 5 5 5
1,944
512
210
A 27
76
15. 32 63
19. Which numbers are two of the prime
A
12. 2 2 19
3,025
Problem Solving and Test Prep
311; 177,147 pennies
21. Which is greater than 92?
11. 52 112
375
PW72
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_C11_L07.indd PW71
6/28/07 1:12:26 PM
MXENL08AWK5X_PHTE_C11_L08.indd PW72
Lesson 11.7
Item
Practice
© Harcourt • Grade 5
6/15/07 2:25:34 PM
Lesson 11.8
Suggested rationale
1
write 5 to the 3rd power in
exponent form and find the
value
2
write 2 to the 2nd power in
exponent form and find the
value
5
find the value of a squared
number
9
find the value of 11 to the
5th power
20
use exponents to solve a
word problem
21
find a number in exponent
form that is greater than 9²
Item
Suggested rationale
2
has 2 prime factors
6
one prime factor is squared
7
one prime factor is squared,
the other prime factor is
cubed
10
multiply to find the number
for the prime factorization
11
multiply to find the number
for the prime factorization
when the prime factors are
written in exponent form
13
find the product
17
use logical reasoning to solve
a word problem
20
test prep
PW71-PW72
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_RatA.indd PW72
7/2/07 3:02:23 PM