Name _______________________________________ Date __________________ Class __________________
Exponents and Roots
SECTION A Family Letter: Exponents
Dear Family,
The student will be learning about exponents and the properties
associated with them. An exponent is a number that represents
how many times the base is to be multiplied by itself. A number
produced by raising a base to an exponent is called a power.
Using exponents will allow the student to write repeated
multiplication in a more efficient way. This is how the student
will write and evaluate exponents.
Vocabulary
These are the math
words we are learning:
scientific notation
a shorthand way of
writing very large or
very small numbers
using powers of 10
Write in exponential form.
2•2•2•2
2 • 2 • 2 • 2  24
Identify how many times 2 is a factor.
Simplify 43.
43  4 • 4 • 4
Find the product of three 4’s.
 64
Sometimes the exponent will be zero. The zero power of any
number except 0 equals 1.
When simplifying expressions with exponents, remind the
student to follow the order of operations.
There are important relationships that exist between exponents
and the operations of multiplication and division. The student
will learn how to multiply and divide powers with the same
base by using some of these basic properties of exponents.
Multiplying
When multiplying powers with the same base, keep the base
constant and add the exponents.
Multiply. Write the product as one power.
56 • 52
562
Add the exponents.
58
Dividing
When dividing powers with the same base, keep the base
constant and subtract the exponents.
Divide. Write the quotient as one power.
1214
129
1214–9
Subtract the exponents.
125
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Exponents and Roots
SECTION A Family Letter: Exponents continued
When multiplying or dividing powers with the same base it is
important to remember not to multiply or divide the bases. This
property only applies when bases are the same. Powers with unlike
bases cannot be combined using the two properties shown in the
examples.
It is possible to raise a power to a power. To simplify a power raised
to a power, keep the base and multiply the exponents.
Since it is possible to have a sum or difference that is a negative
number, the student will learn how to evaluate expressions with
negative exponents. A number raised to a negative exponent equals
1 divided by that number raised to the opposite of the exponent. This
is how the student will learn to evaluate expressions with negative
exponents.
Divide. Write the quotient as one power.
54
56
52 The bases are the same so subtract the exponents.
1
Write the reciprocal and change the sign of the exponent.
52
1
Simplify.
25
Scientific notation is a shorthand way to write very small or very
large numbers. Numbers in scientific notation are written as the
product of a decimal and ten with an exponent.
To change numbers from scientific notation to standard notation,
move the decimal point the number of places indicated by the
exponent, to the right for a positive exponent and to the left for a
negative exponent. Similarly, to convert numbers from standard to
scientific notation, move the decimal point and multiply by ten to the
power of the number of places the decimal point moves.
Multiplying and dividing numbers in scientific notation works the
same way as with other exponents.
Have the student explain the purpose of exponents and the many
ways they are used in mathematics. Verbalizing this information
helps understanding this material.
Sincerely,
Ms. Galanis
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Exponents and Roots
SECTION A At-Home Practice: Exponents
Write using exponents.
1. (4) • (4) • (4)
2. 3 • 3 • 3 • 3 • 3 • 3
_______________
3. 9 • 9
_______________
4. t • t • t
_______________
________________
Simplify.
5. 43
6. (3)4
_______________
9. (2  43)
7. 64
_______________
10. (27 – 32)
_______________
8. (1)9
_______________
11. 25 + (8 • 43)
_______________
________________
12. (12  72)
_______________
________________
Multiply. Write the product as one power.
13. 64 • 63
14. 53 • 56
_______________
15. 82 • 87
_______________
16. k8 • k2
_______________
________________
Divide. Write the quotient as one power.
17.
56
54
18.
_______________
r7
r6
19.
_______________
812
20.
86
_______________
p8
p4
________________
Simplify the powers of 10.
21. 103
22. 106
_______________
23. 108
_______________
24. 101
_______________
________________
Simplify.
25. 33
26.
_______________
62
6
27.
5
_______________
45
4
28. 74 • 75
3
_______________
________________
Write each number in standard or scientific notation.
29. 9,630,000
_______________________
30. 2.7  105
________________________
31. 0.0015
________________________
Answers: 1. (4)3 2. 36 3. 92 4. t3 5. 64 6. 81 7. 1296 8. 1 9. 66 10. 18 11. 537 12. 37 13. 67 14. 59
1
1
15. 89 16. k10 17. 52 18. r 19. 86 20. p4 21. 0.001 22. 0.000001 23. 0.00000001 24. 0.1 25.
26.
216
27
1
27. 16 28.
29. 9.63  106 30. 0.000027 31. 1.5  103
7
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Exponents and Roots
Family Fun: Match It Up!
Directions
Using the numbers in the right-hand column, make the number
sentences true in the left-hand column. You may use some numbers
more than one time and some numbers not at all. See how well you
can match up the correct answers to the number sentences.
Number Sentences
1. 3x 
x equals ______________
Possible Answers for x
0
10
1
9
2. 7.2  10x  0.072
5
3. x12  1
2
4. 8x  83  82
7
5. x4  10,000
3
6.
78
7x
4
1
 49
7. 0.001  10x
5
8. 5x  625
3
9. 12  24 • x1
2
10. 6x • 63  36
6
11.
12.
153
15 x
4
1
1
 10x
10,000
1
10
Answers: 1. 2 2. 2 3. 1 4. 5 5. 10 6. 6 7. 3 8. 4 9. 2 10. 5 11. 3 12. 4
Holt McDougal Mathematics