Download Exponents and Square Numbers

Grade5.indd 36
base
4. 27
Find the value.
1. 5 3 5 3 5 3 5 3 5 3 5 3 5
5. 123
RW71
2. 8 3 8 3 8
6. 192
6/14/07 9:29:08 AM
© Harcourt • Grade 5
Reteach
3. 2 3 2 3 2 3 2 3 2
Exponent form: 63
Words: the third power of six
or six cubed
Write in exponent form and then write in words.
Exponent form: 42
Words: the second power or four
or four squared
Write 4 3 4 and 6 3 6 3 6 in exponent form and in words.
There are two ways to write the word form for an exponent of 2 or 3.
A perfect square or a square number
is the product of a number and itself.
A square number can be represented
with the exponent 2.
36 in words is “the sixth power of three.”
The exponent 6 means “the sixth power.”
Write 36 in words.
A base with an exponent can be written in words.
3 3 3 3 3 3 3 3 3 3 3= 36
The base is repeated 6 times, so 6 is the exponent.
3 is the repeated factor, so 3 is the base.
exponent
A factor tree is a diagram that shows the prime factorization of a composite number.
In the last lesson, the base was always 10. The base does not always have to be 10, though.
36
Prime factorization is a way to show a composite number as the product of prime factors.
You already know that an exponent is a number that tells how many times
the base is used as a factor.
3
3 2 3
3
3
2. 20
5. 3 3 5 3 3 3 5
MXENL08AWK5X_RT_CH11_L08.indd 1
7. 52 3 7
RW72
8. 2 3 3 3 5 3 2 3 7 3 3
Find the number for each prime factorization.
4. 2 3 3 3 5 3 5
Rewrite the prime factorization using exponents.
1. 42
Find the prime factorization. You may use a factor tree.
2 3 2 3 3 = 22 3 3
Rewrite 2 3 2 3 3 using exponents.
You can use exponents in prime factorization for factors that
appear two or more times.
9. 23 3 3 3 112
© Harcourt • Grade 5
Reteach
6. 2 3 5 3 3 3 5 3 2 3 5
3. 90
Write each composite number as a product of two factors.
Write the number as a product of two factors.
Write the number being factored at the top.
So, the prime factorization of 12 is 2 3 2 3 3.
2
4
12
Find the prime factorization of 12. You may use a factor tree.
Prime Factorization
Exponents and Square Numbers
Write 3 3 3 3 3 3 3 3 3 3 3 in exponent form.
Name
Name
MXENL08AWK5X_RT_CH11_L07.indd 1
RW71-RW72
7/19/07 5:58:33 PM
6/14/07 9:32:17 AM
Grade5.indd 36
base
128
4. 27
Find the value.
57; the
seventh
power of five
1. 5 3 5 3 5 3 5 3 5 3 5 3 5
RW71
1,728
5. 123
83; the third
power of eight,
or eight cubed
2. 8 3 8 3 8
361
6. 192
6/14/07 9:29:08 AM
© Harcourt • Grade 5
Reteach
25; the
fifth power
of 2
3. 2 3 2 3 2 3 2 3 2
Exponent form: 63
Words: the third power of six
or six cubed
Write in exponent form and then write in words.
Exponent form: 42
Words: the second power or four
or four squared
Write 4 3 4 and 6 3 6 3 6 in exponent form and in words.
There are two ways to write the word form for an exponent of 2 or 3.
A perfect square or a square number
is the product of a number and itself.
A square number can be represented
with the exponent 2.
36 in words is “the sixth power of three.”
The exponent 6 means “the sixth power.”
Write 36 in words.
A base with an exponent can be written in words.
3 3 3 3 3 3 3 3 3 3 3= 36
The base is repeated 6 times, so 6 is the exponent.
3 is the repeated factor, so 3 is the base.
exponent
A factor tree is a diagram that shows the prime factorization of a composite number.
In the last lesson, the base was always 10. The base does not always have to be 10, though.
36
Prime factorization is a way to show a composite number as the product of prime factors.
You already know that an exponent is a number that tells how many times
the base is used as a factor.
3
3 2 3
3
3
23235
2. 20
32 3 52
5. 3 3 5 3 3 3 5
MXENL08AWK5X_RT_CH11_L08.indd 1
175
7. 52 3 7
RW72
1,260
8. 2 3 3 3 5 3 2 3 7 3 3
Find the number for each prime factorization.
2 3 3 3 52
4. 2 3 3 3 5 3 5
Rewrite the prime factorization using exponents.
23337
1. 42
Find the prime factorization. You may use a factor tree.
2 3 2 3 3 = 22 3 3
Rewrite 2 3 2 3 3 using exponents.
You can use exponents in prime factorization for factors that
appear two or more times.
2,904
9. 23 3 3 3 112
2 2 3 3 3 53
© Harcourt • Grade 5
Reteach
6. 2 3 5 3 3 3 5 3 2 3 5
2333335
3. 90
Write each composite number as a product of two factors.
Write the number as a product of two factors.
Write the number being factored at the top.
So, the prime factorization of 12 is 2 3 2 3 3.
2
4
12
Find the prime factorization of 12. You may use a factor tree.
Prime Factorization
Exponents and Square Numbers
Write 3 3 3 3 3 3 3 3 3 3 3 in exponent form.
Name
Name
MXENL08AWK5X_RT_CH11_L07.indd 1
RW71-RW72
7/19/07 5:58:33 PM
6/14/07 9:32:17 AM