Question 1

Decide whether the expression has been simplified correctly.
-$\left(\frac{\mathrm{a}}{5}\right)^{4}=\frac{\mathrm{a}^{4}}{5}$

Accepted Answer

A) True 
 B)False

Question 2

Choose the one alternative that best completes the statement or answers the question
-$(3+4)^{-1}$

Accepted Answer

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

Question 3

Complete the division.

Accepted Answer

The answer of Complete the division.
  ...

Question 4

For the given pair of functions, find the requested function.
-If $f(x)=x^{2}-x-6$ and $g(x)=x-1$, find $(f g)(x)$.

Accepted Answer

A)  $x^{3}-2 x^{2}-6 x+6$ 
B)  $x^{3}-2 x^{2}-7 x-6$ 
C)  $x^{3}-5 x+6$ 
D)  $x^{3}-2 x^{2}-5 x+6$ 
A)  $x^{3}-2 x^{2}-6 x+6$ 
B)  $x^{3}-2 x^{2}-7 x-6$ 
C)  $x^{3}-5 x+6$ 
D)  $x^{3}-2 x^{2}-5 x+6$

Question 5

Express the number in scientific notation
-736.098

Accepted Answer

A)  $7.36098 \times 10^{1}$ 
B)  $7.36098 \times 10^{2}$ 
C)  $7.36098 \times 10^{-1}$ 
D)  $7.36098 \times 10^{-2}$ 
A)  $7.36098 \times 10^{1}$ 
B)  $7.36098 \times 10^{2}$ 
C)  $7.36098 \times 10^{-1}$ 
D)  $7.36098 \times 10^{-2}$

Question 6

Give the numerical coefficient and the degree of the term.
-$-\mathrm{mn}^{2}$

Accepted Answer

A)  Coefficient: -1 ; degree: 2 
B)  Coefficient: - $m$; degree: 3 
C)  Coefficient: $-m$; degree: 2 
D)  Coefficient: -1 ; degree: 3 
A)  Coefficient: -1 ; degree: 2 
B)  Coefficient: - $m$; degree: 3 
C)  Coefficient: $-m$; degree: 2 
D)  Coefficient: -1 ; degree: 3

Question 7

Find the requested value.
-If $f(x)=x^{2}+3 x+6$ and $g(x)=4 x-1$, find ( $f g(x)$.

Accepted Answer

A)  $4 x^{3}-11 x^{2}-21 x-6$ 
B)  $16 x^{2}+4 x+4$ 
C)  $4 x^{3}+11 x^{2}+3 x-1$ 
D)  $4 x^{3}+11 x^{2}+21 x-6$ 
A)  $4 x^{3}-11 x^{2}-21 x-6$ 
B)  $16 x^{2}+4 x+4$ 
C)  $4 x^{3}+11 x^{2}+3 x-1$ 
D)  $4 x^{3}+11 x^{2}+21 x-6$

Question 8

For the polynomial function, find the requested value.
-$f(x)=3 x^{2}-5 x-3 ; f(2)$

Accepted Answer

A)  -11 
B)  -7 
C)  -5 
D)  -1 
A)  -11 
B)  -7 
C)  -5 
D)  -1

Question 9

Give the domain and range of the function.
-$f(x)=-x^{3}+7$

Accepted Answer

A)  Domain: $(-7, \infty)$; range: $(-\infty, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty, 7)$ 
C)  Domain: $(-\infty, \infty)$; range: $(0, \infty)$ 
D)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$ 
A)  Domain: $(-7, \infty)$; range: $(-\infty, \infty)$ 
B)  Domain: $(-\infty, \infty)$; range: $(-\infty, 7)$ 
C)  Domain: $(-\infty, \infty)$; range: $(0, \infty)$ 
D)  Domain: $(-\infty, \infty)$; range: $(-\infty, \infty)$

Question 10

Find the product
-$(-5 x+11 y)(4 x+10 y+1)$

Accepted Answer

A)  $-20 x^{2}-6 x y-5 x+110 y^{2}+11 y$ 
B)  $-20 x^{2}-50 x y-5 x+110 y^{2}$ 
C)  $-20 x^{2}-6 x y-6 y^{2}$ 
D)  $-20 x^{2}+44 x y-5 x+110 y^{2}+11 y$ 
A)  $-20 x^{2}-6 x y-5 x+110 y^{2}+11 y$ 
B)  $-20 x^{2}-50 x y-5 x+110 y^{2}$ 
C)  $-20 x^{2}-6 x y-6 y^{2}$ 
D)  $-20 x^{2}+44 x y-5 x+110 y^{2}+11 y$

Question 11

Find the product
-$(n-9)(n+9)$

Accepted Answer

A)  $n^{2}-18 n+81$ 
B)  $n^{2}-18$ 
C)  $n^{2}-81$ 
D)  $n^{2}-18 n-81$ 
A)  $n^{2}-18 n+81$ 
B)  $n^{2}-18$ 
C)  $n^{2}-81$ 
D)  $n^{2}-18 n-81$

Question 12

Find the product
-$(x-2)(3 x-1)$

Accepted Answer

A)  $3 x^{2}-7 x-7$ 
B)  $3 x^{2}-7 x+2$ 
C)  $3 x^{2}+2 x-7$ 
D)  $3 x^{2}-9 x+2$ 
A)  $3 x^{2}-7 x-7$ 
B)  $3 x^{2}-7 x+2$ 
C)  $3 x^{2}+2 x-7$ 
D)  $3 x^{2}-9 x+2$

Question 13

Choose the one alternative that best completes the statement or answers the question
-$(-8)^{-2}$

Accepted Answer

A)  -64 
B)  $-\frac{1}{64}$ 
C)  $\frac{1}{64}$ 
D)  64 
A)  -64 
B)  $-\frac{1}{64}$ 
C)  $\frac{1}{64}$ 
D)  64

Question 14

For the polynomial function, find the requested value.
-$f(x)=2 x^{3}-6 x^{2}-21 ; f(4)$

Accepted Answer

A)  1 
B)  -1 
C)  83 
D)  11 
A)  1 
B)  -1 
C)  83 
D)  11

Question 15

Find the product
-$\left(2 \mathrm{~m}^{2}\right)\left(4 \mathrm{~m}^{2}\right)$

Accepted Answer

A)  $-8 m^{4}$ 
B)  $8 \mathrm{~m}$ 
C)  $-8 \mathrm{~m}$ 
D)  $8 m^{4}$ 
A)  $-8 m^{4}$ 
B)  $8 \mathrm{~m}$ 
C)  $-8 \mathrm{~m}$ 
D)  $8 m^{4}$

Question 16

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
-$\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}$

Accepted Answer

A)  $\frac{7}{13 r^{2}}$ 
B)  $\frac{7 \mathrm{r}^{19}}{13}$ 
C)  $\frac{7 \mathrm{r}^{2}}{13}$ 
D)  $\frac{7}{13 r^{19}}$ 
A)  $\frac{7}{13 r^{2}}$ 
B)  $\frac{7 \mathrm{r}^{19}}{13}$ 
C)  $\frac{7 \mathrm{r}^{2}}{13}$ 
D)  $\frac{7}{13 r^{19}}$

Question 17

Express the number in scientific notation
-0.000087719

Accepted Answer

A)  $8.7719 \times 10^{-5}$ 
B)  $8.7719 \times 10^{4}$ 
C)  $8.7719 \times 10^{5}$ 
D)  $8.7719 \times 10^{-4}$ 
A)  $8.7719 \times 10^{-5}$ 
B)  $8.7719 \times 10^{4}$ 
C)  $8.7719 \times 10^{5}$ 
D)  $8.7719 \times 10^{-4}$

Question 18

Express the number in scientific notation
-$-67,000$

Accepted Answer

A)  $-6.7 \times 10^{-5}$ 
B)  $-6.7 \times 10^{5}$ 
C)  $-6.7 \times 10^{-4}$ 
D)  $-6.7 \times 10^{4}$ 
A)  $-6.7 \times 10^{-5}$ 
B)  $-6.7 \times 10^{5}$ 
C)  $-6.7 \times 10^{-4}$ 
D)  $-6.7 \times 10^{4}$

Question 19

Solve the problem. Express your answer in scientific notation, rounding as needed.
-The national debt of a small country is $\$ 6,460,000,000$ and the population is $2,586,000$. What is the amount of debt per person?

Accepted Answer

A)  $\$ 2.50 \times 10^{3}$ 
B)  $\$ 2.50 \times 10^{2}$ 
C)  $\$ 2.50 \times 10^{4}$ 
D)  $\$ 2.50 \times 10^{6}$ 
A)  $\$ 2.50 \times 10^{3}$ 
B)  $\$ 2.50 \times 10^{2}$ 
C)  $\$ 2.50 \times 10^{4}$ 
D)  $\$ 2.50 \times 10^{6}$

Question 20

Choose the one alternative that best completes the statement or answers the question
-$7^{-2}$

Accepted Answer

A)  49 
B)  $\frac{1}{49}$ 
C)  -49 
D)  $-\frac{1}{49}$ 
A)  49 
B)  $\frac{1}{49}$ 
C)  -49 
D)  $-\frac{1}{49}$

Decide whether the expression has been simplified correctly. - $\left(\frac{\mathrm{a}}{5}\right)^{4}=\frac{\mathrm{a}^{4}}{5}$

Choose the one alternative that best completes the statement or answers the question - $(3+4)^{-1}$

Complete the division.

For the given pair of functions, find the requested function. -If $f(x)=x^{2}-x-6$ and $g(x)=x-1$ , find $(f g)(x)$ .

Express the number in scientific notation -736.098

Give the numerical coefficient and the degree of the term. - $-\mathrm{mn}^{2}$

Find the requested value. -If $f(x)=x^{2}+3 x+6$ and $g(x)=4 x-1$ , find ( $f g(x)$ .

For the polynomial function, find the requested value. - $f(x)=3 x^{2}-5 x-3 ; f(2)$

Give the domain and range of the function. - $f(x)=-x^{3}+7$

Find the product - $(-5 x+11 y)(4 x+10 y+1)$

Find the product - $(n-9)(n+9)$

Find the product - $(x-2)(3 x-1)$

Choose the one alternative that best completes the statement or answers the question - $(-8)^{-2}$

For the polynomial function, find the requested value. - $f(x)=2 x^{3}-6 x^{2}-21 ; f(4)$

Find the product - $\left(2 \mathrm{~m}^{2}\right)\left(4 \mathrm{~m}^{2}\right)$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}$

Express the number in scientific notation -0.000087719

Express the number in scientific notation - $-67,000$

Solve the problem. Express your answer in scientific notation, rounding as needed. -The national debt of a small country is $\$ 6,460,000,000$ and the population is $2,586,000$ . What is the amount of debt per person?

Choose the one alternative that best completes the statement or answers the question - $7^{-2}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

Decide whether the expression has been simplified correctly. - (a5)4=a45\left(\frac{\mathrm{a}}{5}\right)^{4}=\frac{\mathrm{a}^{4}}{5}(5a​)4=5a4​

Choose the one alternative that best completes the statement or answers the question - (3+4)−1(3+4)^{-1}(3+4)−1

Complete the division.

For the given pair of functions, find the requested function. -If f(x)=x2−x−6f(x)=x^{2}-x-6f(x)=x2−x−6 and g(x)=x−1g(x)=x-1g(x)=x−1 , find (fg)(x)(f g)(x)(fg)(x) .

Express the number in scientific notation -736.098

Give the numerical coefficient and the degree of the term. - −mn2-\mathrm{mn}^{2}−mn2

Find the requested value. -If f(x)=x2+3x+6f(x)=x^{2}+3 x+6f(x)=x2+3x+6 and g(x)=4x−1g(x)=4 x-1g(x)=4x−1 , find ( fg(x)f g(x)fg(x) .

For the polynomial function, find the requested value. - f(x)=3x2−5x−3;f(2)f(x)=3 x^{2}-5 x-3 ; f(2)f(x)=3x2−5x−3;f(2)

Give the domain and range of the function. - f(x)=−x3+7f(x)=-x^{3}+7f(x)=−x3+7

Find the product - (−5x+11y)(4x+10y+1)(-5 x+11 y)(4 x+10 y+1)(−5x+11y)(4x+10y+1)

Find the product - (n−9)(n+9)(n-9)(n+9)(n−9)(n+9)

Find the product - (x−2)(3x−1)(x-2)(3 x-1)(x−2)(3x−1)

Choose the one alternative that best completes the statement or answers the question - (−8)−2(-8)^{-2}(−8)−2

For the polynomial function, find the requested value. - f(x)=2x3−6x2−21;f(4)f(x)=2 x^{3}-6 x^{2}-21 ; f(4)f(x)=2x3−6x2−21;f(4)

Find the product - (2 m2)(4 m2)\left(2 \mathrm{~m}^{2}\right)\left(4 \mathrm{~m}^{2}\right)(2 m2)(4 m2)

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - 7r−2(r4)413(r−1)5\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}13(r−1)57r−2(r4)4​

Express the number in scientific notation -0.000087719

Express the number in scientific notation - −67,000-67,000−67,000

Solve the problem. Express your answer in scientific notation, rounding as needed. -The national debt of a small country is $6,460,000,000\$ 6,460,000,000$6,460,000,000 and the population is 2,586,0002,586,0002,586,000 . What is the amount of debt per person?

Choose the one alternative that best completes the statement or answers the question - 7−27^{-2}7−2

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Decide whether the expression has been simplified correctly. - $\left(\frac{\mathrm{a}}{5}\right)^{4}=\frac{\mathrm{a}^{4}}{5}$

Choose the one alternative that best completes the statement or answers the question - $(3+4)^{-1}$

For the given pair of functions, find the requested function. -If $f(x)=x^{2}-x-6$ and $g(x)=x-1$ , find $(f g)(x)$ .

Give the numerical coefficient and the degree of the term. - $-\mathrm{mn}^{2}$

Find the requested value. -If $f(x)=x^{2}+3 x+6$ and $g(x)=4 x-1$ , find ( $f g(x)$ .

For the polynomial function, find the requested value. - $f(x)=3 x^{2}-5 x-3 ; f(2)$

Give the domain and range of the function. - $f(x)=-x^{3}+7$

Find the product - $(-5 x+11 y)(4 x+10 y+1)$

Find the product - $(n-9)(n+9)$

Find the product - $(x-2)(3 x-1)$

Choose the one alternative that best completes the statement or answers the question - $(-8)^{-2}$

For the polynomial function, find the requested value. - $f(x)=2 x^{3}-6 x^{2}-21 ; f(4)$

Find the product - $\left(2 \mathrm{~m}^{2}\right)\left(4 \mathrm{~m}^{2}\right)$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}$

Express the number in scientific notation - $-67,000$

Solve the problem. Express your answer in scientific notation, rounding as needed. -The national debt of a small country is $\$ 6,460,000,000$ and the population is $2,586,000$ . What is the amount of debt per person?

Choose the one alternative that best completes the statement or answers the question - $7^{-2}$