Practice Makes Perfect
Use the Definition of a Negative Exponent
In the following exercises, simplify.
Exercise 2
- 3−4
- 10−2
- Answer
-
- 181
- 1100
Exercise 4
- 2−8
- 10−2
- Answer
-
- 1256
- 1100
Exercise 6
- 1c−5
- 15−2
- Answer
-
- c5
- 25
Exercise 8
- 1t−9
- 110−4
- Answer
-
- t9
- 10000
Exercise 9
- (58)−2
- (−3mn)−2
Exercise 10
- (310)−2
- (−2cd)−3
- Answer
-
- 1009
- −d38c3
Exercise 11
- (49)−3
- (−u22v)−5
Exercise 12
- (72)−3
- (−3xy2)−3
- Answer
-
- 8343
- −x3y627
Exercise 13
- (−5)−2
- −5−2
- (−15)−2
- −(15)−2
Exercise 14
- (−7)−2
- −7−2
- (−17)−2
- −(17)−2
- Answer
-
- 149
- −149
- 49
- −49
Exercise 15
- −3−3
- (−13)−3
- −(13)−3
- (−3)−3
Exercise 16
- −5−3
- (−15)−3
- −(15)−3
- (−5)−3
- Answer
-
- −1125
- −125
- −125
- −1125
Exercise 17
- 3·5−1
- (3·5)−1
Exercise 18
- 2·5−1
- (2·5)−1
- Answer
-
- 25
- 110
Exercise 19
- 4·5−2
- (4·5)−2
Exercise 20
- 3·4−2
- (3·4)−2
- Answer
-
- 316
- 1144
Exercise 22
- b−5
- (k2)−5
- Answer
-
- 1b5
- 1k10
Exercise 24
- s−8
- (a9)−10
- Answer
-
- 1s8
- 1a90
Exercise 25
- 7n−1
- (7n)−1
- (−7n)−1
Exercise 26
- 6r−1
- (6r)−1
- (−6r)−1
- Answer
-
- 6r
- 16r
- −16r
Exercise 27
- (3p)−2
- 3p−2
- −3p−2
Exercise 28
- (2q)−4
- 2q−4
- −2q−4
- Answer
-
- 116q4
- 2q4
- −2q4
Simplify Expressions with Integer Exponents
In the following exercises, simplify.
Exercise 29
- b4b−8
- r−2r5
- x−7x−3
Exercise 30
- s3·s−7
- q−8·q3
- y−2·y−5
- Answer
-
- 1s4
- 1q5
- 1y7
Exercise 31
- a3·a−3
- a·a3
- a·a−3
Exercise 32
- y5·y−5
- y·y5
- y·y−5
- Answer
-
- 1
- y6
- 1y4
Exercise 34
x4·x−2·x−3
- Answer
-
1x
Exercise 35
(w4x−5)(w−2x−4)
Exercise 36
(m3n−3)(m−5n−1)
- Answer
-
1m2n4
Exercise 37
(uv−2)(u−5v−3)
Exercise 38
(pq−4)(p−6q−3)
- Answer
-
1p5q7
Exercise 39
(−6c−3d9)(2c4d−5)
Exercise 40
(−2j−5k8)(7j2k−3)
- Answer
-
−14k5j3
Exercise 41
(−4r−2s−8)(9r4s3)
Exercise 42
(−5m4n6)(8m−5n−3)
- Answer
-
−40n3m
Exercise 44
(4y3)−3
- Answer
-
164y9
Exercise 46
(2p−5)2
- Answer
-
4p10
Exercise 48
n5n−2
- Answer
-
n7
Exercise 50
y−5y−10
- Answer
-
y5
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
Exercise 52
340,000
- Answer
-
3.4×105
Exercise 54
1,290,000
- Answer
-
1.29×106
Exercise 56
0.041
- Answer
-
4.1×10−2
Exercise 58
0.00000103
- Answer
-
1.03×10−6
Convert Scientific Notation to Decimal Form
In the following exercises, convert each number to decimal form.
Exercise 60
8.3×102
- Answer
-
830
Exercise 62
1.6×1010
- Answer
-
16,000,000,000
Exercise 64
3.8×10−2
- Answer
-
0.038
Exercise 66
1.93×10−5
- Answer
-
0.0000193
Multiply and Divide Using Scientific Notation
In the following exercises, multiply. Write your answer in decimal form.
Exercise 67
(3×10−5)(3×109)
Exercise 68
(2×102)(1×10−4)
- Answer
-
0.02
Exercise 69
(7.1×10−2)(2.4×10−4)
Exercise 70
(3.5×10−4)(1.6×10−2)
- Answer
-
5.6×10−6
In the following exercises, divide. Write your answer in decimal form.
Exercise 72
5×10−21×10−10
- Answer
-
500,000,000
Exercise 74
8×1064×10−1
- Answer
-
20,000,000
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?