Prealgebra

Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price

Chapter 4 Factors and Fractions - all with Video Answers

Educators

Section 1

Powers and Exponents

00:16

Problem 1

Write each expression using exponents.
$$n \cdot n \cdot n$$

Julie Silva

Numerade Educator

00:13

Problem 2

Write each expression using exponents.
$$7 \cdot 7$$

Julie Silva

Numerade Educator

00:14

Problem 3

Write each expression using exponents.
$$(-4)(-4)(-4)$$

Julie Silva

Numerade Educator

00:22

Problem 4

Write each expression using exponents.
$$3 \cdot 3 \cdot x \cdot x \cdot x \cdot x$$

Julie Silva

Numerade Educator

00:17

Problem 5

Write each expression using exponents.
$$(y-3)(y-3)(y-3)$$

Julie Silva

Numerade Educator

00:17

Problem 6

Write each expression using exponents.
$$(a+1)(a+1)$$

Julie Silva

Numerade Educator

00:22

Problem 7

Evaluate each expression.
$$2^{4}$$

Julie Silva

Numerade Educator

00:20

Problem 8

Evaluate each expression.
$$6^{3}$$

Julie Silva

Numerade Educator

00:22

Problem 9

Evaluate each expression.
$$2 \cdot 5^{2}$$

Julie Silva

Numerade Educator

00:46

Problem 10

Evaluate each expression if $x=-2$ and $y=4$
$$x^{3}-4$$

Julie Silva

Numerade Educator

00:53

Problem 11

Evaluate each expression if $x=-2$ and $y=4$
$$5(y-1)^{2}$$

Julie Silva

Numerade Educator

00:59

Problem 12

Evaluate each expression if $x=-2$ and $y=4$
$$x^{2}+y^{2}$$

Julie Silva

Numerade Educator

00:36

Problem 13

SOUND Fireworks can easily reach a sound of 169 decibels, which can be dangerous if prolonged. Write this number using a power greater than 1 and a lesser base.

Julie Silva

Numerade Educator

00:20

Problem 14

Write each expression using exponents.
$$4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$$

Julie Silva

Numerade Educator

00:19

Problem 15

Write each expression using exponents.
$$6$$

Julie Silva

Numerade Educator

00:20

Problem 16

Write each expression using exponents.
$$(-5)(-5)(-5)$$

Julie Silva

Numerade Educator

00:19

Problem 17

Write each expression using exponents.
$$(-8)(-8)(-8)(-8)$$

Julie Silva

Numerade Educator

00:18

Problem 18

Write each expression using exponents.
$$k \cdot k$$

Julie Silva

Numerade Educator

00:21

Problem 19

Write each expression using exponents.
$$(-t)(-t)(-t)$$

Julie Silva

Numerade Educator

00:19

Problem 20

Write each expression using exponents.
$$r \cdot r \cdot r \cdot r$$

Julie Silva

Numerade Educator

00:18

Problem 21

Write each expression using exponents.
$$m \cdot m \cdot m \cdot m$$

Julie Silva

Numerade Educator

00:25

Problem 22

Write each expression using exponents.
$$a \cdot a \cdot b \cdot b \cdot b \cdot b$$

Julie Silva

Numerade Educator

00:36

Problem 23

Write each expression using exponents.
$$2 \cdot x \cdot x \cdot y \cdot y$$

Julie Silva

Numerade Educator

00:18

Problem 24

Write each expression using exponents.
$$(n-5)(n-5)(n-5)$$

Julie Silva

Numerade Educator

00:29

Problem 25

Write each expression using exponents.
$$9 \cdot(p+1) \cdot(p+1)$$

Julie Silva

Numerade Educator

00:14

Problem 26

Evaluate each expression.
$$7^{2}$$

Julie Silva

Numerade Educator

00:21

Problem 27

Evaluate each expression.
$$10^{3}$$

Julie Silva

Numerade Educator

00:27

Problem 28

Evaluate each expression.
$$(-9)^{3}$$

Julie Silva

Numerade Educator

00:33

Problem 29

Evaluate each expression.
$$(-2)^{5}$$

Julie Silva

Numerade Educator

00:24

Problem 30

Evaluate each expression.
$$3 \cdot 4^{2}$$

Julie Silva

Numerade Educator

00:40

Problem 31

Evaluate each expression.
$$2 \cdot 4^{3}$$

Julie Silva

Numerade Educator

00:40

Problem 32

Evaluate each expression.
$$6^{3} \cdot 4$$

Julie Silva

Numerade Educator

00:54

Problem 33

Evaluate each expression.
$$3^{5} \cdot 10$$

Julie Silva

Numerade Educator

00:20

Problem 34

Evaluate each expression.
$$2^{0} \cdot 10$$

Julie Silva

Numerade Educator

00:46

Problem 35

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$b^{4}$$

Julie Silva

Numerade Educator

00:49

Problem 36

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$c^{4}$$

Julie Silva

Numerade Educator

00:42

Problem 37

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$4 a^{4}$$

Julie Silva

Numerade Educator

00:53

Problem 38

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$a c^{3}$$

Julie Silva

Numerade Educator

00:31

Problem 39

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$b^{0}-10$$

Julie Silva

Numerade Educator

00:52

Problem 40

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$c^{2}+a^{2}$$

Julie Silva

Numerade Educator

00:57

Problem 41

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$3 a+b^{3}$$

Julie Silva

Numerade Educator

00:45

Problem 42

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$a^{2}+3 a-1$$

Julie Silva

Numerade Educator

00:49

Problem 43

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$b^{2}-2 b+6$$

Julie Silva

Numerade Educator

00:55

Problem 44

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$3(b-1)^{4}$$

Julie Silva

Numerade Educator

01:01

Problem 45

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$2(3 c+7)^{2}$$

Julie Silva

Numerade Educator

00:46

Problem 46

Evaluate each expression if $a=2, b=4,$ and $c=-3$
$$5\left(a^{3}+6\right)$$

Julie Silva

Numerade Educator

00:50

BIOLOGY A man burns approximately 121 Calories by standing for an hour. A woman burns approximately 100 Calories per hour when standing. Write each of these numbers as a power with an exponent greater than 1

Julie Silva

Numerade Educator

02:35

Problem 48

MILEAGE Which numbers in the table can be expressed as a power greater than $1 ?$ Name the cities and express the numbers as powers.

Julie Silva

Numerade Educator

00:39

Problem 49

Write 7 cubed times $x$ squared as repeated multiplication.

Julie Silva

Numerade Educator

00:42

Problem 50

Write negative eight cubed using exponents and as a product of repeated factors.

Julie Silva

Numerade Educator

02:02

Problem 51

Without using a calculator, order $96,96^{2}, 96^{10}$ $96^{5},$ and $96^{0}$ from least to greatest. Explain.

Ashley Volpe

Numerade Educator

00:50

Problem 52

NUMBER THEORY Explain whether the square of any nonzero number is sometimes, always, or never a positive number.

Julie Silva

Numerade Educator

01:25

Problem 53

In an ancient Chinese tradition, a chef stretches and folds dough to make long, thin noodles called so. After the first fold, he makes 2 noodles. He stretches and folds it a second time to make 4 noodles. Each time he repeats this process, the number of noodles doubles.
Use exponents to express the number of noodles after each of the first five folds.

Julie Silva

Numerade Educator

01:51

Problem 54

Use the following information.
In an ancient Chinese tradition, a chef stretches and folds dough to make long, thin noodles called so. After the first fold, he makes 2 noodles. He stretches and folds it a second time to make 4 noodles. Each time he repeats this process, the number of noodles doubles.
Legendary chefs have completed as many as thirteen folds. How many noodles is this?

Julie Silva

Numerade Educator

02:28

Problem 55

Use the following information.
In an ancient Chinese tradition, a chef stretches and folds dough to make long, thin noodles called so. After the first fold, he makes 2 noodles. He stretches and folds it a second time to make 4 noodles. Each time he repeats this process, the number of noodles doubles.
If the noodles are laid end to end and each noodle is 5 feet long, after how many of these folds will the length be more than a mile?

Julie Silva

Numerade Educator

00:58

Problem 56

Replace each $\cdot$ with $<,>,$ or $=$ to make a true statement.
$$3^{7} \cdot 7^{3}$$

Julie Silva

Numerade Educator

00:33

Problem 57

Replace each $\cdot$ with $<,>,$ or $=$ to make a true statement.
$$2^{4} \cdot 4^{2}$$

Julie Silva

Numerade Educator

00:34

Problem 58

Replace each $\cdot$ with $<,>,$ or $=$ to make a true statement.
$$6^{3} \cdot 4^{4}$$

Julie Silva

Numerade Educator

01:02

Problem 59

Use the cube at the right.
(Cube can't copy)
The surface area of a cube is the sum of the areas of the faces. Use exponents to write an expression for the surface area of the cube.

Julie Silva

Numerade Educator

00:36

Problem 60

Use the cube at the right.
(Cube can't copy)
The volume of a cube, or the amount of space that it occupies, is the product of the length, width, and height. Use exponents to write an expression for the volume of the cube.

Julie Silva

Numerade Educator

01:50

Problem 61

Use the cube at the right.
(Cube can't copy)
If you double the length of each edge of the cube, are the surface area and volume also doubled? Explain.

Julie Silva

Numerade Educator

01:01

Problem 62

OPEN ENDED Use exponents to write a numerical expression and an algebraic expression in which the base is a factor 5 times.

Julie Silva

Numerade Educator

01:48

Problem 63

CHALLENGE Suppose the length of a side of a square is $n$ units and the length of an edge of a cube is $n$ units.
(Cube can't copy)
If all the side lengths of a square are doubled, are the perimeter and the area of the square doubled? Explain.

Julie Silva

Numerade Educator

00:57

Problem 64

CHALLENGE Suppose the length of a side of a square is $n$ units and the length of an edge of a cube is $n$ units.
(Cube can't copy)
If all the side lengths of a square are tripled, show that the area of the new square is 9 times the area of the original square. Explain.

Julie Silva

Numerade Educator

01:11

Problem 65

CHALLENGE Suppose the length of a side of a square is $n$ units and the length of an edge of a cube is $n$ units.
(Cube can't copy)
If all the edge lengths of a cube are tripled, show that the volume of the new cube is 27 times the volume of the original cube. Explain.

Julie Silva

Numerade Educator

01:13

Problem 66

SELECT A TOOL Mercury has a mean distance from the Sun of $6000^{2}$ miles. Which of the following tools might you use to determine the mean distance from the Sun to Mars if it is four times Mercury's distance to the Sun? Justify your selection(s). Then use the tool(s) to solve the problem.

Julie Silva

Numerade Educator

02:06

Problem 67

Writing in Math Use the information about exponents on page 180 to explain how they are used to describe computer memory. Include an advantage of using exponents.

Julie Silva

Numerade Educator

01:10

Problem 68

Which expression represents the number of cells after half an hour?
A $2^{10}$
B $2^{15}$
C $2^{20}$
D $2^{30}$
$$\begin{array}{|c|c|}
\hline \begin{array}{c}
\text { Time } \\
\text { (min) }
\end{array} & \begin{array}{c}
\text { Number of } \\
\text { Bacteria }
\end{array} \\
\hline 0 & 2^{0} \\
\hline 3 & 2^{1} \\
\hline 6 & 2^{2} \\
\hline 9 & 2^{3} \\
\hline 12 & 2^{4} \\
\hline
\end{array}$$

Julie Silva

Numerade Educator

01:48

Problem 69

GRIDDABLE Suppose a certain forest fire doubles in size every 8 hours. If the initial size of the fire was 1 acre, how many acres will the fire cover in
3 days?

Julie Silva

Numerade Educator

00:44

Problem 70

TORNADOES A tornado travels 300 miles in 2 hours. Use the formula $d=r t$ to find the tornado's speed in miles per hour.

Julie Silva

Numerade Educator

00:57

Problem 71

PATTERNS Study the pattern. Find the equation that represents a relationship between the number of columns $c$ and the number of rows $r$ in the pattern.

Julie Silva

Numerade Educator

00:43