Name ________________________________________ Date ___________________ Class __________________
Review for Mastery
LESSON
6-x
6-1
Integer Exponents
Remember that 23 means 2 × 2 × 2 = 8. The base is 2, the exponent is positive 3.
Exponents can also be 0 or negative.
Zero Exponents
Negative Exponents
Negative Exponents
in the Denominator
For any nonzero For any nonzero number x For any nonzero number
1
x and any integer n,
number x,
and any integer n, x−n = n .
1
x0 = 1.
x
= xn.
x −n
Definition
0
Examples
60 = 1
⎛ 1⎞
⎜2⎟ = 1
⎝ ⎠
5−3 =
1
53
2−4 =
1
24
1
= 82
8−2
1
= 24
2−4
00 and 0−n are undefined.
Simplify 4−2.
4−2
Simplify x2y−3z0.
x2y−3z0
1
42
x 2 z0
y3
Write without negative exponents.
Write without negative
exponents.
2
1
4•4
Write in expanded form.
x (1)
y3
z0 = 1.
1
16
Simplify.
x2
y3
Simplify.
Fill in the blanks to simplify each expression.
1. 2−5
2. 10−3
2−5 =
1
3.
10−3 =
2
1
=
25
1
10
1
=
103
1
= ____________
1
= ____________
1
5−4
1
= 5
5−4
5
=
= ____________
Simplify.
4. 5 y −4
_____________
5.
8
a −3
_____________
6. 9 x 3 y −2
____________
x3
x −1y _____________
8.
b2
a −1b3 _____________
9. 5 x −4 y 2
_____________
7.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
6-6
Holt McDougal Algebra 1
Review for Mastery
1
1. 5; 2•2•2•2•2;
32
1
2. 10•10•10;
1000
5
4. 4
y
3. 4; 4; 5•5•5•5; 625
5. 8a
x4
7.
y
10. 4
11. 512
12. 200
13. −8
14. 324
15.
5. B
6. H
2
liters
3
Reading Strategies
a
8.
b
5y 2
9.
x4
4. 42
7. C
9x3
6.
y2
3
3. 3.142
1. 6
2. 0
3. 8 −3
4.
1
b7
5. 32
6.
1
32
7. 1
8.
1
1,000,000
9. −64
1
16
Challenge
1. 1; 1; 1; 1; 1; 1; 1; 1; 1
2. 2; 4; 8; 6; 2; 4; 8; 6; 2
3. 3; 9; 7; 1; 3; 9; 7; 1; 3
10. −
1
64
c2
d3
11.
1
t4
12.
13.
8
x5
14. 12
6-2 RATIONAL EXPONENTS
4. 4; 6; 4; 6; 4; 6; 4; 6; 4
Practice A
5. 5; 5; 5; 5; 5; 5; 5; 5; 5
6. 6; 6; 6; 6; 6; 6; 6; 6; 6
7. 7; 9; 3; 1; 7; 9; 3; 1; 7
8. 8; 4; 2; 6; 8; 4; 2; 6; 8
9. 9; 1; 9; 1; 9; 1; 9; 1; 9
10. 0; 0; 0; 0; 0; 0; 0; 0; 0
11. For all n, 1n has 1 as its units digit.
1. B
2. D
3. C
4. A
5. 7
6. 3
7. 1
8. 12
9. 8
10. 9
11. 1
12. 32
13. x
12. The pattern is 2, 4, 8, and 6, for n = 1, 2,
3, and 4 and then repeats.
8
15. m4n
14. x3y4
16. x2
17. 14 cm
13. The pattern is 3, 9, 7, and 1, for n = 1, 2,
3, and 4 and then repeats.
Practice B
n
14. For all n > 0, 5 has 5 as its units digit.
1. 3
2. 11
15. If you divide n by 4, then the units digit is
7, 9, 3, or 1, depending on whether the
remainder is 1, 2, 3, or 0, respectively.
3. 0
4. 11
5. 4
6. 8
Problem Solving
1.
4
or 0.16 mm 2
25
2.
3
3
and
oz
8
4
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A2
Holt McDougal Algebra 1
Name ________________________________________ Date ___________________ Class __________________
Review for Mastery
LESSON
6-x
6-1
Integer Exponents continued
Evaluate a−3b4 for a = 5 and b = 2.
a−3b4
(5−3)(24)
4
2
53
16
125
Substitute.
Write without negative exponents.
Simplify.
When evaluating, it is important to determine whether the negative is raised to the power.
Evaluate −x−2 for x = 10.
Evaluate (−x)−2 for x = 10.
The negative is not raised
to the power.
The negative is raised to
the power.
−x−2
−10−2
−
−
1
102
1
10 • 10
−
1
100
(−x)−2
(−10)−2
Substitute.
1
( −10)2
Write without negative
exponents
1
( −10) • ( −10)
Write in expanded form.
1
100
Simplify.
Substitute.
Write without negative
exponents
Write in expanded form.
Simplify.
Evaluate each expression for the given value(s) of the variable(s).
10. x2y0 for x = −2 and y = 5
11. a3b3 for a = 4 and b = 2
_________________________________________
12.
z3
for z = 2 and y = 5
y −2
13. −a3b−4 for a = 2 and b = −1
_________________________________________
14.
________________________________________
−2
n
for m = 6 and n = 2
m −4
________________________________________
15. (−u)2v−6 for u = 2 and v = 2
_________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
6-7
Holt McDougal Algebra 1