Beginning and Intermediate Algebra: An Integrated Approach

R. David Gustafson, Peter D. Frisk

Chapter 4

Polynomials - all with Video Answers

Educators

Section 1

Natural-Number Exponents

Problem 1

Graph the real numbers $-3,0,2$, and $-\frac{3}{2}$ on a number line.
( graph can't copy )

Sherrie Fenner

Sherrie Fenner

Numerade Educator

Problem 2

Graph the real numbers $-2<x \leq 3$ on a number line.
( graph can't copy )

Yujie Wang

College of San Mateo

Problem 3

Write each algebraic expression as an English phrase.
$3(x+y)$

Katelyn Chen

Numerade Educator

Problem 4

Write each algebraic expression as an English phrase.
$3 x+y$

Rithvik Manne

Numerade Educator

Problem 5

Write each English phrase as an algebraic expression.
Three greater than the absolute value of twice $x$

Julie Silva

Numerade Educator

Problem 6

Write each English phrase as an algebraic expression.
The sum of the numbers $y$ and $z$ decreased by the sum of their squares

Victor Salazar

Numerade Educator

Problem 7

Fill in the blanks.
The base of the exponential expression $(-5)^3$ is _____________ The exponent is -

Amy Jiang

Numerade Educator

Problem 8

Fill in the blanks.
The base of the exponential expression $-5^3$ is - . The exponent is _____________

Erika Bustos

Numerade Educator

Problem 9

Fill in the blanks.
$(3 x)^4$ means _____________

Dale Sanford

Numerade Educator

Problem 10

Fill in the blanks.
Write $(-3 y)(-3 y)(-3 y)$ as a power. _____________

Lois Campbell

Numerade Educator

Problem 11

Fill in the blanks.
$y^5=$ _____________

Kristin Cameron

Kristin Cameron

Numerade Educator

Problem 12

Fill in the blanks.
$x^m x^n=$ _____________

Shaza Hammoud

Numerade Educator

Problem 13

Fill in the blanks.
$(x y)^n=$ _____________

Maninder Singh

Numerade Educator

Problem 14

Fill in the blanks.
$\left(\frac{a}{b}\right)^n=$ _____________

Jeyasree R T

Numerade Educator

Problem 15

Fill in the blanks.
$\left(a^b\right)^c=$ _____________

Jeyasree R T

Numerade Educator

Problem 16

Fill in the blanks.
$\frac{x^m}{x^n}=$ _____________

Dale Sanford

Numerade Educator

Problem 17

The area of the square is $s \cdot s$. Why do you think the symbol $s^2$ is called "s squared"?
( figure can't copy )

Charles Carter

Numerade Educator

Problem 18

The volume of the cube is $s \cdot s \cdot s$. Why do you think the symbol $s^3$ is called " $s$ cubed"?
( figure can't copy )

Savannah Langenstein

Savannah Langenstein

Numerade Educator

Problem 19

Identify the base and the exponent in each expression.
$4^3$

Sherrie Fenner

Numerade Educator

Problem 20

Identify the base and the exponent in each expression.
$(-5)^2$

Sherrie Fenner

Numerade Educator

Problem 21

Identify the base and the exponent in each expression.
$x^5$

Erika Bustos

Numerade Educator

Problem 22

Identify the base and the exponent in each expression.
$y^8$

Lois Campbell

Numerade Educator

Problem 23

Identify the base and the exponent in each expression.
$(2 y)^3$

Anna Myers

Numerade Educator

Problem 24

Identify the base and the exponent in each expression.
$(-3 x)^2$

Sherrie Fenner

Numerade Educator

Problem 25

Identify the base and the exponent in each expression.
$-x^4$

Anna Myers

Numerade Educator

Problem 26

Identify the base and the exponent in each expression.
$(-x)^4$

Erika Bustos

Numerade Educator

Problem 27

Identify the base and the exponent in each expression.
$x$

Erika Bustos

Numerade Educator

Problem 28

Identify the base and the exponent in each expression.
$(x y)^3$

Brandon Fox

Numerade Educator

Problem 29

Identify the base and the exponent in each expression.
$2 x^3$

Dale Sanford

Numerade Educator

Problem 30

Identify the base and the exponent in each expression.
$-3 y^6$

Sherrie Fenner

Numerade Educator

Problem 31

Write each expression without using exponents.
$5^3$

Check back soon!

Problem 32

Write each expression without using exponents.
$-4^5$

Dale Sanford

Numerade Educator

Problem 33

Write each expression without using exponents.
$x^7$

Dale Sanford

Numerade Educator

Problem 34

Write each expression without using exponents.
$3 x^3$

Dale Sanford

Numerade Educator

Problem 35

Write each expression without using exponents.
$-4 x^5$

Dale Sanford

Numerade Educator

Problem 36

Write each expression without using exponents.
$(-2 y)^4$

Dale Sanford

Numerade Educator

Problem 37

Write each expression without using exponents.
$(3 t)^5$

Zach Steedman

Numerade Educator

Problem 38

Write each expression without using exponents.
$a^3 b^2$

Amy Jiang

Numerade Educator

Problem 39

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

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 40

Write each expression using exponents.
$5 \cdot 5$

Julie Silva

Numerade Educator

Problem 41

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

Cory Kuzinski

Numerade Educator

Problem 42

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

Lauren Shelton

Numerade Educator

Problem 43

Write each expression using exponents.
$(2 x)(2 x)(2 x)$

Emily Himsel

Numerade Educator

Problem 44

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

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 45

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

Jeyasree R T

Numerade Educator

Problem 46

Write each expression using exponents.
$5 \cdot u \cdot u$

Jeyasree R T

Numerade Educator

Problem 47

Evaluate each expression.
$5^4$

Check back soon!

Problem 48

Evaluate each expression.
$(-3)^3$

Brandon Fox

Numerade Educator

Problem 49

Evaluate each expression.
$2^2+3^2$

James Kiss

Numerade Educator

Problem 50

Evaluate each expression.
$2^3-2^2$

Margaret Farmer

Margaret Farmer

Numerade Educator

Problem 51

Evaluate each expression.
$5^4-4^3$

Check back soon!

Problem 52

Evaluate each expression.
$2\left(4^3+3^2\right)$

James Kiss

Numerade Educator

Problem 53

Evaluate each expression.
$-5\left(3^4+4^3\right)$

Amy Jiang

Numerade Educator

Problem 54

Evaluate each expression.
$-5^2\left(4^3-2^6\right)$

James Kiss

Numerade Educator

Problem 55

Write each expression as an expression involving only one exponent.
$x^4 x^3$

Hailey Tomashek

Hailey Tomashek

Numerade Educator

Problem 56

Write each expression as an expression involving only one exponent.
$y^5 y^2$

Laura Skalaski

Numerade Educator

Problem 57

Write each expression as an expression involving only one exponent.
$x^5 x^5$

Meredith Moody

Numerade Educator

Problem 58

Write each expression as an expression involving only one exponent.
$y y^3$

Laura Skalaski

Numerade Educator

Problem 59

Write each expression as an expression involving only one exponent.
$t t^2$

Cory Kuzinski

Numerade Educator

Problem 60

Write each expression as an expression involving only one exponent.
$w^3 w^5$

Amy Jiang

Numerade Educator

Problem 61

Write each expression as an expression involving only one exponent.
$a^3 a^4 a^5$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 62

Write each expression as an expression involving only one exponent.
$b^2 b^3 b^5$

Julie Silva

Numerade Educator

Problem 63

Write each expression as an expression involving only one exponent.
$y^3\left(y^2 y^4\right)$

Laura Skalaski

Numerade Educator

Problem 64

Write each expression as an expression involving only one exponent.
$\left(y^4 y\right) y^6$

Jeyasree R T

Numerade Educator

Problem 65

Write each expression as an expression involving only one exponent.
$4 x^2\left(3 x^5\right)$

Dale Sanford

Numerade Educator

Problem 66

Write each expression as an expression involving only one exponent.
$-2 y\left(y^3\right)$

Matt Gibson

Numerade Educator

Problem 67

Write each expression as an expression involving only one exponent.
$\left(-y^2\right)\left(4 y^3\right)$

Zach Steedman

Numerade Educator

Problem 68

Write each expression as an expression involving only one exponent.
$\left(-4 x^3\right)(-5 x)$

Julie Silva

Numerade Educator

Problem 69

Write each expression as an expression involving only one exponent.
$6 x^3\left(-x^2\right)\left(-x^4\right)$

Julie Silva

Numerade Educator

Problem 70

Write each expression as an expression involving only one exponent.
$-2 x\left(-x^2\right)(-3 x)$

Kristin Cameron

Kristin Cameron

Numerade Educator

Problem 71

Write each expression as an expression involving only one exponent.
$\left(3^2\right)^4$

Cory Kuzinski

Numerade Educator

Problem 72

Write each expression as an expression involving only one exponent.
$\left(4^3\right)^3$

Cory Kuzinski

Numerade Educator

Problem 73

Write each expression as an expression involving only one exponent.
$\left(y^5\right)^3$

Jeyasree R T

Numerade Educator

Problem 74

Write each expression as an expression involving only one exponent.
$\left(b^3\right)^6$

Jeyasree R T

Numerade Educator

Problem 75

Write each expression as an expression involving only one exponent.
$\left(a^3\right)^7$

Sherrie Fenner

Numerade Educator

Problem 76

Write each expression as an expression involving only one exponent.
$\left(b^2\right)^3$

Katelyn Chen

Numerade Educator

Problem 77

Write each expression as an expression involving only one exponent.
$\left(x^2 x^3\right)^5$

Jeyasree R T

Numerade Educator

Problem 78

Write each expression as an expression involving only one exponent.
$\left(y^3 y^4\right)^4$

Jeyasree R T

Numerade Educator

Problem 79

Write each expression as an expression involving only one exponent.
$\left(3 z z^2 z^3\right)^5$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 80

Write each expression as an expression involving only one exponent.
$\left(4 t^3 t^6 t^2\right)^2$

Jeyasree R T

Numerade Educator

Problem 81

Write each expression as an expression involving only one exponent.
$\left(x^5\right)^2\left(x^7\right)^3$

Oluwaseyitan Balogun

Oluwaseyitan Balogun

Numerade Educator

Problem 82

Write each expression as an expression involving only one exponent.
$\left(y^3 y\right)^2\left(y^2\right)^2$

Jeyasree R T

Numerade Educator

Problem 83

Write each expression as an expression involving only one exponent.
$\left(r^3 r^2\right)^4\left(r^3 r^5\right)^2$

Laura Skalaski

Numerade Educator

Problem 84

Write each expression as an expression involving only one exponent.
$\left(s^2\right)^3\left(s^3\right)^2\left(s^4\right)^4$

Jeyasree R T

Numerade Educator

Problem 85

Write each expression as an expression involving only one exponent.
$\left(s^3\right)^3\left(s^2\right)^2\left(s^5\right)^4$

Jeyasree R T

Numerade Educator

Problem 86

Write each expression as an expression involving only one exponent.
$\left(y y^3\right)^3\left(y^2 y^3\right)^4\left(y^3 y^3\right)^2$

Maninder Singh

Numerade Educator

Problem 87

Write each expression without parentheses.
$(x y)^3$

Kristin Cameron

Kristin Cameron

Numerade Educator

Problem 88

Write each expression without parentheses.
$\left(u v^2\right)^4$

Julie Silva

Numerade Educator

Problem 89

Write each expression without parentheses.
$\left(r^3 s^2\right)^2$

Cory Kuzinski

Numerade Educator

Problem 90

Write each expression without parentheses.
$\left(a^3 b^2\right)^3$

Matt Gibson

Numerade Educator

Problem 91

Write each expression without parentheses.
$\left(4 a b^2\right)^2$

Erika Bustos

Numerade Educator

Problem 92

Write each expression without parentheses.
$\left(3 x^2 y\right)^3$

Erika Bustos

Numerade Educator

Problem 93

Write each expression without parentheses.
$\left(-2 r^2 s^3 t\right)^3$

Amy Jiang

Numerade Educator

Problem 94

Write each expression without parentheses.
$\left(-3 x^2 y^4 z\right)^2$

Maninder Singh

Numerade Educator

Problem 95

Write each expression without parentheses.
$\left(\frac{a}{b}\right)^3$

Nick Johnson

Numerade Educator

Problem 96

Write each expression without parentheses.
$\left(\frac{r^2}{s}\right)^4$

Cory Kuzinski

Numerade Educator

Problem 97

Write each expression without parentheses.
$\left(\frac{x^2}{y^3}\right)^5$

Jeyasree R T

Numerade Educator

Problem 98

Write each expression without parentheses.
$\left(\frac{u^4}{v^2}\right)^6$

Jeyasree R T

Numerade Educator

Problem 99

Write each expression without parentheses.
$\left(\frac{-2 a}{b}\right)^5$

Nick Johnson

Numerade Educator

Problem 100

Write each expression without parentheses.
$\left(\frac{2 t}{3}\right)^4$

Nick Johnson

Numerade Educator

Problem 101

Write each expression without parentheses.
$\left(\frac{b^2}{3 a}\right)^3$

Erika Bustos

Numerade Educator

Problem 102

Write each expression without parentheses.
$\left(\frac{a^3 b}{c^4}\right)^5$

Brandon Fox

Numerade Educator

Problem 103

Simplify each expression.
$\frac{x^5}{x^3}$

Erika Bustos

Numerade Educator

Problem 104

Simplify each expression.
$\frac{a^6}{a^3}$

Brandon Fox

Numerade Educator

Problem 105

Simplify each expression.
$\frac{y^3 y^4}{y y^2}$

Erika Bustos

Numerade Educator

Problem 106

Simplify each expression.
$\frac{b^4 b^5}{b^2 b^3}$

Jeyasree R T

Numerade Educator

Problem 107

Simplify each expression.
$\frac{12 a^2 a^3 a^4}{4\left(a^4\right)^2}$

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 108

Simplify each expression.
$\frac{16\left(a a^2\right)^3}{2 a^2 a^3}$

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 109

Simplify each expression.
$\frac{\left(a b^2\right)^3}{(a b)^2}$

Matt Gibson

Numerade Educator

Problem 110

Simplify each expression.
$\frac{\left(m^3 n^4\right)^3}{\left(m n^2\right)^3}$

Jeyasree R T

Numerade Educator

Problem 111

Simplify each expression.
$\frac{20\left(r^4 s^3\right)^4}{6\left(r s^3\right)^3}$

Brandon Fox

Numerade Educator

Problem 112

Simplify each expression.
$\frac{15\left(x^2 y^5\right)^5}{21\left(x^3 y\right)^2}$

Anas Venkitta

Numerade Educator

Problem 113

Simplify each expression.
$\frac{17\left(x^4 y^3\right)^8}{34\left(x^5 y^2\right)^4}$

Lourence Gonhovi

Lourence Gonhovi

Numerade Educator

Problem 114

Simplify each expression.
$\frac{35\left(r^3 s^2\right)^2}{49 r^2 s^3}$

Brandon Fox

Numerade Educator

Problem 115

Simplify each expression.
$\left(\frac{y^3 y}{2 y y^2}\right)^3$

Jeyasree R T

Numerade Educator

Problem 116

Simplify each expression.
$\left(\frac{3 t^3 t^4 t^5}{4 t^2 t^6}\right)^3$

Sherrie Fenner

Numerade Educator

Problem 117

Simplify each expression.
$\left(\frac{-2 r^3 r^3}{3 r^4 r}\right)^3$

Sherrie Fenner

Numerade Educator

Problem 118

Simplify each expression.
$\left(\frac{-6 y^4 y^5}{5 y^3 y^5}\right)^2$

Rukhmani Jain

Numerade Educator

Problem 119

Bouncing balls When a certain ball is dropped, it always rebounds to one-half of its previous height. If the ball is dropped from a height of 32 feet, explain why the expression $32\left(\frac{1}{2}\right)^4$ represents the height of the ball on the fourth bounce. Find the height of the fourth bounce.

Vikash Ranjan

Numerade Educator

Problem 120

Having babies The probability that a couple will have $n$ baby boys in a row is given by the formula $\left(\frac{1}{2}\right)^n$. Find the probability that a couple will have four baby boys in a row.

Melissa Lupinacci

Melissa Lupinacci

Numerade Educator

Problem 121

Investing If an investment of $$\$ 1,000$$ doubles every seven years, find the value of the investment after 28 years.
If $P$ dollars are invested at a rate $r$, compounded annually, it will grow to $A$ dollars in t years according to the formula
$$
A=P(1+r)^t
$$

Carson Merrill

Numerade Educator

Problem 122

___________ Compound interest How much will be in an account at the end of 2 years if $$\$ 12,000$$ is invested at $5 \%$, compounded annually?

Jennifer Stoner

Jennifer Stoner

Numerade Educator

Problem 123

___________ Compound interest How much will be in an account at the end of 30 years if $$\$ 8,000$$ is invested at $6 \%$, compounded annually?

Grant Mansfield

Grant Mansfield

Numerade Educator

Problem 124

___________ Investing Guess the answer to the following problem. Then use a calculator to find the correct answer. Were you close? If the value of $1 \nmid$ is to double every day, what will the penny be worth after 31 days?

Cory Kuzinski

Numerade Educator

Problem 125

Describe how you would multiply two exponential expressions with like bases.

Ashley Hanson

Numerade Educator

Problem 126

Describe how you would divide two exponential expressions with like bases.

Christopher Stanley

Christopher Stanley

Numerade Educator

Problem 127

Is the operation of raising to a power commutative? That is, is $a^b=b^a$ ? Explain.

Rachel Mcmahon

Numerade Educator

Problem 128

Is the operation of raising to a power associative? That is, is $\left(a^b\right)^c=a^{(b)}$ ? Explain.

Matt Gibson

Numerade Educator