Question 1

Identify the coefficient of each term of the polynomial.
-$- 5 z - 3 y$

Accepted Answer

A)  $- 5$ and 3 
B)  5 and 3 
C)  5 and $- 3$ 
D)  $- 5$ and $- 3$ 
A)  $- 5$ and 3 
B)  5 and 3 
C)  5 and $- 3$ 
D)  $- 5$ and $- 3$

Question 2

Simplify.
-$\left( \frac { a ^ { 3 } } { b ^ { 4 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { a ^ { 4 } } { b ^ { 8 } }$ 
B)  $\frac { a ^ { 6 } } { b ^ { 8 } }$ 
C)  $\frac { a ^ { 8 } } { b ^ { 6 } }$ 
D)  $\frac { a ^ { 6 } } { b ^ { 4 } }$ 
A)  $\frac { a ^ { 4 } } { b ^ { 8 } }$ 
B)  $\frac { a ^ { 6 } } { b ^ { 8 } }$ 
C)  $\frac { a ^ { 8 } } { b ^ { 6 } }$ 
D)  $\frac { a ^ { 6 } } { b ^ { 4 } }$

Question 3

Evaluate.
-$( - 12 ) ^ { 0 }$

Accepted Answer

A)  $- 12$ 
B)  1 
C)  0 
D)  $- 1$ 
A)  $- 12$ 
B)  1 
C)  0 
D)  $- 1$

Question 4

Evaluate.
-The volume of a cylinder with height $h$ and radius $r$ is given by $V = \pi r ^ { 2 } h$. Find the volume of the cylinder. Use $3.14$ for $\pi$.

Accepted Answer

A)  $347 \mathrm { ft } ^ { 3 }$ 
B)  $9021.2 \mathrm { ft } ^ { 3 }$ 
C)  $693.9 \mathrm { ft } ^ { 3 }$ 
D)  $2255.3 \mathrm { ft } ^ { 3 }$ 
A)  $347 \mathrm { ft } ^ { 3 }$ 
B)  $9021.2 \mathrm { ft } ^ { 3 }$ 
C)  $693.9 \mathrm { ft } ^ { 3 }$ 
D)  $2255.3 \mathrm { ft } ^ { 3 }$

Question 5

Write the number in scientific notation.
-0.000281

Accepted Answer

A)  $2.81 \times 10 ^ { 4 }$ 
B)  $2.81 \times 10 ^ { - 5 }$ 
C)  $2.81 \times 10 ^ { - 4 }$ 
D)  $2.81 \times 10 ^ { - 3 }$ 
A)  $2.81 \times 10 ^ { 4 }$ 
B)  $2.81 \times 10 ^ { - 5 }$ 
C)  $2.81 \times 10 ^ { - 4 }$ 
D)  $2.81 \times 10 ^ { - 3 }$

Question 6

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
-$$9 x ^ { 3 } + 3 w ^ { 2 } - 7 w - 5 w ^ { 4 } - 2$$

Accepted Answer

A)  Trinomial, degree 4 
B)  None, degree 4 
C)  Binomial, degree 11 
D)  Trinomial, degree 10 
A)  Trinomial, degree 4 
B)  None, degree 4 
C)  Binomial, degree 11 
D)  Trinomial, degree 10

Question 7

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
-$16 a ^ { 8 }$

Accepted Answer

A)  Monomial, degree 16 
B)  Binomial, degree 8 
C)  Monomial, degree 8 
D)  Binomial, degree 16 
A)  Monomial, degree 16 
B)  Binomial, degree 8 
C)  Monomial, degree 8 
D)  Binomial, degree 16

Question 8

Simplify.
-$\left( - 3 p ^ { 6 } q ^ { 6 } r ^ { 6 } \right) ^ { 3 }$

Accepted Answer

A)  $- 9 p ^ { 9 } q ^ { 9 } r ^ { 9 }$ 
B)  $( - 3 ) ^ { 3 } \mathrm { p } ^ { 9 } \mathrm { q } ^ { 9 } \mathrm { r } ^ { 9 }$ 
C)  $( - 3 ) ^ { 3 } \mathrm { p } ^ { 18 } \mathrm { q } ^ { 18 } \mathrm { r } 18$ 
D)  $( - 3 ) ^ { 18 } \mathrm { p } ^ { 18 } \mathrm { q } ^ { 18 } \mathrm { r } ^ { 18 }$ 
A)  $- 9 p ^ { 9 } q ^ { 9 } r ^ { 9 }$ 
B)  $( - 3 ) ^ { 3 } \mathrm { p } ^ { 9 } \mathrm { q } ^ { 9 } \mathrm { r } ^ { 9 }$ 
C)  $( - 3 ) ^ { 3 } \mathrm { p } ^ { 18 } \mathrm { q } ^ { 18 } \mathrm { r } 18$ 
D)  $( - 3 ) ^ { 18 } \mathrm { p } ^ { 18 } \mathrm { q } ^ { 18 } \mathrm { r } ^ { 18 }$

Question 9

Simplify.
-$$\left( - 2 p ^ { - 3 } q ^ { 3 } r ^ { - 3 } \right) ^ { 5 }$$

Accepted Answer

A)  $\frac { ( - 2 ) ^ { 5 } p ^ { 15 } } { q ^ { 15 } r ^ { 15 } }$ 
B)  $\frac { ( - 2 ) ^ { 5 } q ^ { 15 } } { p ^ { 15 } + 15 }$ 
C)  $\frac { ( - 2 ) ^ { 5 } } { p ^ { 15 } q ^ { 15 } r 15 }$ 
D)  $( - 2 ) ^ { 5 } p ^ { 15 _ { q } } 15 _ { \mathbf { r } } 15$ 
A)  $\frac { ( - 2 ) ^ { 5 } p ^ { 15 } } { q ^ { 15 } r ^ { 15 } }$ 
B)  $\frac { ( - 2 ) ^ { 5 } q ^ { 15 } } { p ^ { 15 } + 15 }$ 
C)  $\frac { ( - 2 ) ^ { 5 } } { p ^ { 15 } q ^ { 15 } r 15 }$ 
D)  $( - 2 ) ^ { 5 } p ^ { 15 _ { q } } 15 _ { \mathbf { r } } 15$

Question 10

Divide and simplify.
-$\frac { t ^ { - 3 } } { t ^ { - 8 } }$

Accepted Answer

A)  $t ^ { 11 }$ 
B)  $t ^ { - 11 }$ 
C)  $t ^ { 5 }$ 
D)  $t ^ { - 5 }$ 
A)  $t ^ { 11 }$ 
B)  $t ^ { - 11 }$ 
C)  $t ^ { 5 }$ 
D)  $t ^ { - 5 }$

Question 11

Express using positive exponents. Then simplify.
-$\frac { 1 } { x ^ { - 2 } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $x ^ { 2 }$ 
C)  $x ^ { - 2 }$ 
D)  $2 x$ 
A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $x ^ { 2 }$ 
C)  $x ^ { - 2 }$ 
D)  $2 x$

Question 12

Evaluate.
-The volume of a cube with sides of length $s$ is given by $V = s ^ { 3 }$. Find the volume of the cube.

Accepted Answer

A)  $19,683 \mathrm { ft } ^ { 3 }$ 
B)  $729 \mathrm { ft } ^ { 3 }$ 
C)  $81 \mathrm { ft } ^ { 3 }$ 
D)  $1458 \mathrm { ft } ^ { 3 }$ 
A)  $19,683 \mathrm { ft } ^ { 3 }$ 
B)  $729 \mathrm { ft } ^ { 3 }$ 
C)  $81 \mathrm { ft } ^ { 3 }$ 
D)  $1458 \mathrm { ft } ^ { 3 }$

Question 13

Convert to decimal notation.
-$10 ^ { - 6 }$

Accepted Answer

A)  $0.000001$ 
B)  $0.00001$ 
C)  $0.0001$ 
D)  $0.0000001$ 
A)  $0.000001$ 
B)  $0.00001$ 
C)  $0.0001$ 
D)  $0.0000001$

Question 14

Evaluate.
-$\left( \frac { 2 } { 7 } \right) ^ { 1 }$

Accepted Answer

A)  $\frac { 7 } { 2 }$ 
B)  $- \frac { 2 } { 7 }$ 
C)  1 
D)  $\frac { 2 } { 7 }$ 
A)  $\frac { 7 } { 2 }$ 
B)  $- \frac { 2 } { 7 }$ 
C)  1 
D)  $\frac { 2 } { 7 }$

Question 15

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-The earth is approximately $92,900,000$ miles from the sun. If 1 mile $= 1.61 \times 10 ^ { 3 } \mathrm {~m}$, what is the distance to the sun in meters?

Accepted Answer

A)  $5.7 \times 10 ^ { - 10 } \mathrm {~m}$ 
B)  $1.50 \times 10^{10} \mathrm {~m}$ 
C)  $5.7 \times 10^{10} \mathrm {~m}$ 
D)  $1.50 \times 10^{11} \mathrm {~m}$ 
A)  $5.7 \times 10 ^ { - 10 } \mathrm {~m}$ 
B)  $1.50 \times 10^{10} \mathrm {~m}$ 
C)  $5.7 \times 10^{10} \mathrm {~m}$ 
D)  $1.50 \times 10^{11} \mathrm {~m}$

Question 16

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-Assume that the volume of the earth is $5 \times 10 ^ { 14 }$ cubic meters and the volume of a bacterium is $2.5 \times 10 ^ { - 16 }$ cubic meters. If the earth could be filled with bacteria, how many would it contain?

Accepted Answer

A)  $5.0 \times 10 ^ { 31 }$ bacteria 
B)  $2.0 \times 10 ^ { - 30 }$ bacteria 
C)  $2.0 \times 10 ^ { 30 }$ bacteria 
D)  $5.0 \times 10 ^ { - 31 }$ bacteria 
A)  $5.0 \times 10 ^ { 31 }$ bacteria 
B)  $2.0 \times 10 ^ { - 30 }$ bacteria 
C)  $2.0 \times 10 ^ { 30 }$ bacteria 
D)  $5.0 \times 10 ^ { - 31 }$ bacteria

Question 17

Evaluate the polynomial.
-$6 - \frac { 1 } { 9 } x$, when $x = 0$

Accepted Answer

A)  6 
B)  $- \frac { 1 } { 9 }$ 
C)  0 
D)  $- 6$ 
A)  6 
B)  $- \frac { 1 } { 9 }$ 
C)  0 
D)  $- 6$

Question 18

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-The life span of the average male human being is approximately 37,843,200 minutes.

Accepted Answer

A)  $37.8432 \times 10 ^ { 6 }$ minutes 
B)  $3.78432 \times 10 ^ { 6 }$ minutes 
C)  $3.78432 \times 10 ^ { 7 }$ minutes 
D)  $3.78432 \times 10 ^ { 5 }$ minutes 
A)  $37.8432 \times 10 ^ { 6 }$ minutes 
B)  $3.78432 \times 10 ^ { 6 }$ minutes 
C)  $3.78432 \times 10 ^ { 7 }$ minutes 
D)  $3.78432 \times 10 ^ { 5 }$ minutes

Question 19

Solve the problem.
-During the first seconds, the height $h$ in feet of a baseball after $t$ seconds is given by $h = - 16 t ^ { 2 } + 99 t + 4.4$. Use the graph below to estimate the height of the ball after 3 seconds.

Accepted Answer

A)  157 feet 
B)  139 feet 
C)  193 feet 
D)  $- 144$ feet 
A)  157 feet 
B)  139 feet 
C)  193 feet 
D)  $- 144$ feet

Question 20

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-The speed of light is $1.86 \times 10 ^ { 5 }$ miles per hour.

Accepted Answer

A)  $1,860,000$ 
B)  $0.0000186$ 
C)  $18,600,000$ 
D)  186,000 
A)  $1,860,000$ 
B)  $0.0000186$ 
C)  $18,600,000$ 
D)  186,000

Identify the coefficient of each term of the polynomial. - $- 5 z - 3 y$

Simplify. - $\left( \frac { a ^ { 3 } } { b ^ { 4 } } \right) ^ { 2 }$

Evaluate. - $( - 12 ) ^ { 0 }$

Write the number in scientific notation. -0.000281

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - $9 x ^ { 3 } + 3 w ^ { 2 } - 7 w - 5 w ^ { 4 } - 2$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - $16 a ^ { 8 }$

Simplify. - $\left( - 3 p ^ { 6 } q ^ { 6 } r ^ { 6 } \right) ^ { 3 }$

Simplify. - $\left( - 2 p ^ { - 3 } q ^ { 3 } r ^ { - 3 } \right) ^ { 5 }$

Divide and simplify. - $\frac { t ^ { - 3 } } { t ^ { - 8 } }$

Express using positive exponents. Then simplify. - $\frac { 1 } { x ^ { - 2 } }$

Evaluate. -The volume of a cube with sides of length $s$ is given by $V = s ^ { 3 }$ . Find the volume of the cube. $Evaluate. -The volume of a cube with sides of length s is given by V = s ^ { 3 } . Find the volume of the cube.$

Convert to decimal notation. - $10 ^ { - 6 }$

Evaluate. - $\left( \frac { 2 } { 7 } \right) ^ { 1 }$

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -The earth is approximately $92,900,000$ miles from the sun. If 1 mile $= 1.61 \times 10 ^ { 3 } \mathrm {~m}$ , what is the distance to the sun in meters?

Evaluate the polynomial. - $6 - \frac { 1 } { 9 } x$ , when $x = 0$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The life span of the average male human being is approximately 37,843,200 minutes.

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -The speed of light is $1.86 \times 10 ^ { 5 }$ miles per hour.

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

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Exam 4: Polynomials: Operations

Identify the coefficient of each term of the polynomial. - −5z−3y- 5 z - 3 y−5z−3y

Simplify. - (a3b4)2\left( \frac { a ^ { 3 } } { b ^ { 4 } } \right) ^ { 2 }(b4a3​)2

Evaluate. - (−12)0( - 12 ) ^ { 0 }(−12)0

Evaluate. -The volume of a cylinder with height hhh and radius rrr is given by V=πr2hV = \pi r ^ { 2 } hV=πr2h . Find the volume of the cylinder. Use 3.143.143.14 for π\piπ .