Name: __________________________________________
Int Math 2 Handout (Lesson 3.1)
What is each expression written using each base only once?
1
8
8 ⋅8
4
A
512
B
8
C
24
D
8
2
7
12
32
12
12
10
⋅7
−4
⋅7
7
13
A
343
B
7
13
C
7
−280
D
21
13
What is the simplified form of each expression?
3
4
2b
−1
⋅ 5b
9
A
10b
8
10
x ⋅ 2y
A
10
⋅ 5x
80
10x y
−10
B
7b
B
10xy
9
C
7b
C
10x y
−10
D
10b
D
8x y
5
10
23
13
10
13
10
Find the simplified form of the expression. Give your answer in scientific notation.
5
6
ÊÁ
ˆÊ
ˆ
ÁÁ 7 × 10 2 ˜˜˜ ÁÁÁ 7 × 10 5 ˜˜˜
ÁË
˜¯ ÁË
˜¯
A
1.4 × 10
8
B
4.9 × 10
8
C
1.4 × 10
11
D
4.9 × 10
11
7
ÊÁ
ˆÊ
ˆ
ÁÁ 3 × 10 −6 ˜˜˜ ÁÁÁ 6 × 10 −8 ˜˜˜
ÁË
˜¯ ÁË
˜¯
−15
A
1.8 × 10
B
18 × 10
C
1.8 × 10
−16
D
1.8 × 10
−13
−13
1
ÊÁ
ˆÊ
ˆ
ÁÁ 9 × 10 5 ˜˜˜ ÁÁÁ 6 × 10 −7 ˜˜˜
ÁË
˜¯ ÁË
˜¯
A
5.4 × 10
−1
B
5.4 × 10
−34
C
1.5 × 10
−1
D
1.5 × 10
−34
Name: ______________________
8
ID: A
5
Last year, a large trucking company delivered 5.5 × 10 tons of goods with an average value of
$23,000 per ton. What was the total value of the goods delivered? Write the answer in scientific
notation.
A
1.265 × 10
11
dollars
C
1.265 × 10 dollars
9
B
1.265 × 10
10
dollars
D
1.265 × 10
12
dollars
What is the simplified form of the expression?
9
6 2
−5
ÁÊÁ 7 ˜ˆ˜
Á
˜
3Á 5 ˜
12 k ÁÁÁÁ k ˜˜˜˜
ÁÁ
˜˜
ÁÁ
˜˜
Ë
¯
1
A
(p )
12
A
p
B
2p
C
p
36
D
p
8
12
k
B
5
3
1
5
10 (t )
A
B
C
D
C
1
t
k
1
4
1
1
4
k
3
13
1
3
ˆ −9
7Ê 2
11 m ÁÁÁÁ m ˜˜˜˜
Ë ¯
A
4
D
3
t
t
3
t
k
4
ÊÁ
Á
ÊÁ 6 ˆ˜ ÁÁÁ
ÁÁ 2x ˜˜ ÁÁ 3x
ÁË
˜¯ ÁÁ
ÁÁ
ÁË
A
6x
C
5x
3
D
6x
3
5
B
m
C
m
D
m
−11
−49
2
13
2
B
11
m
5x
13
2
1
2
ˆ˜
˜˜
˜˜
˜˜
˜˜
˜˜
˜¯
Name: ______________________
ID: A
What is the simplified form of each expression?
3 4
7
2
14 (3h )
6
2 6
16 (3x ) (x )
12
A
3h
81h
7
A
729x
33
B
81h
12
B
729x
29
C
3h
C
3x
33
D
D
3x
29
81
2 −5
15 (10n )
A
B
−3
100000n
1
−10
n
100000
C
10n
−10
D
10n
32
4
6 2
5
33
37
5 5
17 (−5g h ) (g h )
33
A
25g h
5
5 3
5
16
18
B
25g h
B
216a b
37
C
g h
25
C
216a b
33
D
−25g h
D
27a b
8
37
3 3
18 (2a b ) (3a b )
A
30
−216a b
24
16
14
30
19 Suppose a white dwarf star has a diameter
3
of approximately 1.8083 × 10 km. Use the
2
formula 4 πr to find the approximate surface
area of the star.
approximately 2.4 × 10 m. Use the formula
ÁÊÁ 4 ˜ˆ˜ 3
ÁÁ ˜˜ πr to find the approximate volume of the
ÁÁ 3 ˜˜
Ë ¯
asteroid.
5
A
2.27 × 10 km2
B
1.64 × 10
C
1.03 × 10 km2
10
24
20 Suppose a spherical asteroid has a radius of
4
D
30
24
km2
9
7
1.03 × 10 km2
3
4
A
3.02 × 10 m3
B
5.79 × 10
10
m3
7
C
5.79 × 10 m3
D
3.71 × 10
12
m3
Name: ______________________
ID: A
What is the simplified form of each expression?
21
t
11
t
24
2
9
A
t
B
t
1
c d
9
−7
14
−10
c d
A
13
C
t
t
D
B
9
C
22
D
22
y
−2
y
5
7
y
3
B
y
C
y
1
7
D
q
2
d
4
2
c d
d
3
c
5
4
3
y
23
d
3
25 Scientists believe that there is an extremely
massive black hole at the center of the Milky
Way. How many times more massive than the
Sun would a black hole with a mass of
36
7.36 × 10 kg be? The mass of the Sun is
30
approximately 1.99 × 10 kg.
1
A
5
c d
33
4
q
A
3.7 × 10
3
B
3.7 × 10
4
66
C
3.7 × 10
6
D
3.7 × 10
8
66
8
1
A
q
B
q
1
C
q
D
q
1/4
1/4
What is the simplified form of the expression?
26
ÊÁ b
ÁÁ
ÁÁ
ÁË 7
ˆ˜ 2
˜˜
˜˜
˜¯
2
A
b
14
2
B
b
7
2
b
49
C
4
D
7b
2
Name: ______________________
27
ÊÁ
ÁÁ 3
ÁÁ
ÁÁ 9
ÁË 5y
ˆ˜ 3
˜˜
˜˜
˜˜
˜¯
27
A
27
125y
28
ÊÁ 4
ÁÁ 4k
ÁÁ
ÁÁÁ 7c 3
Ë
A
B
B
27
5y
9
C
15y
12
28k c
12k
9
12
64k
D
27
15 y
27
31 Astronomers measure large distances in
light-years. One light-year is the distance that
light can travel in one year, or approximately
12
5.88 × 10 miles. Suppose a star is
3
1.92 × 10 light-years from Earth. In scientific
notation, approximately how many miles is it?
ˆ˜ 3
˜˜
˜˜
˜˜
˜
¯
9
343c
C
ID: A
12
21c
9
12
D
29
64k
7c
ÊÁ 3
ÁÁ m
ÁÁ
ÁÁ 5
Á 4c
Ë
A
ˆ˜ −4
˜˜
˜˜
˜˜
˜
¯
20
12
−16m
4c
30
B
256c
m
B
A
20
C
256m
4c
D
4m
ÊÁ 5
ÁÁ 3x
ÁÁ
ÁÁ 4
Á 8j
Ë
A
B
12
c
20
15 12
24x j
512j
12
15
−24x
9j
D
12
ˆ˜ −3
˜˜
˜˜
˜˜
˜
¯
27x
C
12
15
12
512x
8j
15
5
5.88 × 10
13
miles
5.88 × 10
12
miles
16
C
1.13 × 10 miles
D
1.92 × 10
14
miles