Question 1

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$.
-$f(x)=7 x+6$ and $g(x)=7 x-6$

Accepted Answer

A)  $14 x$ 
B)  12 
C)  $49 x-36$ 
D)  $49 x+36$ 
A)  $14 x$ 
B)  12 
C)  $49 x-36$ 
D)  $49 x+36$

Question 2

Find the result that a calculator will give for the stated problem. Write your answer using the usual scientific notation.
-(7.2E17)/(3E-7)

Accepted Answer

A)  $2.4 \times 10^{-24}$ 
B)  $2.4 \times 10^{10}$ 
C)  $21.6 \times 10^{24}$ 
D)  $2.4 \times 10^{24}$ 
A)  $2.4 \times 10^{-24}$ 
B)  $2.4 \times 10^{10}$ 
C)  $21.6 \times 10^{24}$ 
D)  $2.4 \times 10^{24}$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{18 x^{8}+21 x^{6}+24 x^{4}}{3 x^{6}}$

Accepted Answer

A)  $6 x+7+\frac{8}{x}$ 
B)  $6 x+7+\frac{8}{x^{2}}$ 
C)  $6 x^{2}+7+\frac{8}{x^{2}}$ 
D)  $6 x^{2}+7+\frac{8}{x}$ 
A)  $6 x+7+\frac{8}{x}$ 
B)  $6 x+7+\frac{8}{x^{2}}$ 
C)  $6 x^{2}+7+\frac{8}{x^{2}}$ 
D)  $6 x^{2}+7+\frac{8}{x}$

Question 4

Express the number in standard notation.
-$8.213 \times 10^{-6}$

Accepted Answer

A)  0.000008213 
B)  0.0000008213 
C)  0.00008213 
D)  $-8,213,000$ 
A)  0.000008213 
B)  0.0000008213 
C)  0.00008213 
D)  $-8,213,000$

Question 5

Find the product
-$4 x^{3}(5 x-8)$

Accepted Answer

A)  $-12 x^{4}$ 
B)  $20 x^{4}-32 x^{3}$ 
C)  $20 x^{3}-32$ 
D)  $-20 x^{4}+32 x^{3}$ 
A)  $-12 x^{4}$ 
B)  $20 x^{4}-32 x^{3}$ 
C)  $20 x^{3}-32$ 
D)  $-20 x^{4}+32 x^{3}$

Question 6

Apply the product rule for exponents, if possible.
-$\mathrm{g}^{10} \cdot \mathrm{h}^{8}$

Accepted Answer

A)  The product rule does not apply. 
B)  $\mathrm{gh}^{18}$ 
C)  $\mathrm{g}^{80} \mathrm{~h}$ 
D)  $\mathrm{gh}^{2}$ 
A)  The product rule does not apply. 
B)  $\mathrm{gh}^{18}$ 
C)  $\mathrm{g}^{80} \mathrm{~h}$ 
D)  $\mathrm{gh}^{2}$

Question 7

For what values, if any, of $x(x \neq 0)$ and $n$ will $x^{-n}$ be a negative number?

Accepted Answer

If @#LAT-DLM& is negative and

Question 8

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.
-$\frac{6}{6^{-1}}$

Accepted Answer

A)  The quotient rule does not apply. 
B)  $6^{2}$ 
C)  6 
D)  1 
A)  The quotient rule does not apply. 
B)  $6^{2}$ 
C)  6 
D)  1

Question 9

Find the product
-$(\mathrm{p}+6)^{2}$

Accepted Answer

A)  $p^{2}+36$ 
B)  $p+36$ 
C)  $p^{2}+12 p+36$ 
D)  $36 p^{2}+12 p+36$ 
A)  $p^{2}+36$ 
B)  $p+36$ 
C)  $p^{2}+12 p+36$ 
D)  $36 p^{2}+12 p+36$

Question 10

Perform the indicated operations.
-$(4 x-10)(x-1)$

Accepted Answer

A)  $4 x^{2}-14 x+10$ 
B)  $4 x^{2}-15 x+10$ 
C)  $x^{2}+10 x-14$ 
D)  $x^{2}-14 x-15$ 
A)  $4 x^{2}-14 x+10$ 
B)  $4 x^{2}-15 x+10$ 
C)  $x^{2}+10 x-14$ 
D)  $x^{2}-14 x-15$

Question 11

The fact that $8 ? { 5 6 } = 7$ and $7 ? { 5 6 } = 8$ demonstrates a way to check division. Perform the following division, and then use the above property to check it.

Accepted Answer

The answer of The fact that \(8 ? { 5...

Question 12

Decide whether the expression has been simplified correctly.
-$(6 b)^{2}=6 b^{2}$

Accepted Answer

A) True 
 B)False

Question 13

Decide whether the expression has been simplified correctly.
-$x^{7} \cdot x^{6}=x^{42}$

Accepted Answer

A) True 
 B)False

Question 14

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.
-$\frac{x^{5}}{x^{17}}$

Accepted Answer

A)  $\frac{1}{x^{12}}$ 
B)  $x^{12}$ 
C)  $-x^{12}$ 
D)  $\frac{1}{x^{22}}$ 
A)  $\frac{1}{x^{12}}$ 
B)  $x^{12}$ 
C)  $-x^{12}$ 
D)  $\frac{1}{x^{22}}$

Question 15

For the polynomial function, find the requested value.
-$f(x)=8 x+5 ; f(7)$

Accepted Answer

A)  51 
B)  61 
C)  13 
D)  112 
A)  51 
B)  61 
C)  13 
D)  112

Question 16

$f(x)=x^{2}-3$ and $g(x)=8 x+6$; (g of $)(x)$.

Accepted Answer

A)  $x^{2}-8 x-9$ 
B)  $x^{2}+8 x+3$ 
C)  $8 x^{2}-18$ 
D)  $64 x^{2}+16 x-6$ 
A)  $x^{2}-8 x-9$ 
B)  $x^{2}+8 x+3$ 
C)  $8 x^{2}-18$ 
D)  $64 x^{2}+16 x-6$

Question 17

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\left(4 r^{2}+\frac{45}{7} r-1\right) \div(7 r-1)$

Accepted Answer

A)  $\frac{4}{7} \mathrm{r}+1$ 
B)  $\frac{4}{7} r-1$ 
C)  $-3 r^{2}+\frac{52}{7} r-1$ 
D)  $r^{2}+45 r-1$ 
A)  $\frac{4}{7} \mathrm{r}+1$ 
B)  $\frac{4}{7} r-1$ 
C)  $-3 r^{2}+\frac{52}{7} r-1$ 
D)  $r^{2}+45 r-1$

Question 18

Find the value of the expression.
-$\frac{7 \times 10^{-3}}{28 \times 10^{2}}$

Accepted Answer

A)  -0.0000025 
B)  25,000 
C)  $-25,000$ 
D)  0.0000025 
A)  -0.0000025 
B)  25,000 
C)  $-25,000$ 
D)  0.0000025

Question 19

Combine terms.
-$3 q^{-9}+10 q^{-9}-9 q^{-9}$

Accepted Answer

A)  $-270 q^{-27}$ 
B)  $-270 q^{-9}$ 
C)  $4 q^{-27}$ 
D)  $4 q^{-9}$ 
A)  $-270 q^{-27}$ 
B)  $-270 q^{-9}$ 
C)  $4 q^{-27}$ 
D)  $4 q^{-9}$

Question 20

Choose the one alternative that best completes the statement or answers the question
-$-9^{2}$

Accepted Answer

A)  $-\frac{1}{81}$ 
B)  -81 
C)  81 
D)  $\frac{1}{81}$ 
A)  $-\frac{1}{81}$ 
B)  -81 
C)  81 
D)  $\frac{1}{81}$

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=7 x+6$ and $g(x)=7 x-6$

Find the result that a calculator will give for the stated problem. Write your answer using the usual scientific notation. -(7.2E17)/(3E-7)

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{18 x^{8}+21 x^{6}+24 x^{4}}{3 x^{6}}$

Express the number in standard notation. - $8.213 \times 10^{-6}$

Find the product - $4 x^{3}(5 x-8)$

Apply the product rule for exponents, if possible. - $\mathrm{g}^{10} \cdot \mathrm{h}^{8}$

For what values, if any, of $x(x \neq 0)$ and $n$ will $x^{-n}$ be a negative number?

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{6}{6^{-1}}$

Find the product - $(\mathrm{p}+6)^{2}$

Perform the indicated operations. - $(4 x-10)(x-1)$

The fact that $8 ? { 5 6 } = 7$ and $7 ? { 5 6 } = 8$ demonstrates a way to check division. Perform the following division, and then use the above property to check it.

Decide whether the expression has been simplified correctly. - $(6 b)^{2}=6 b^{2}$

Decide whether the expression has been simplified correctly. - $x^{7} \cdot x^{6}=x^{42}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{5}}{x^{17}}$

For the polynomial function, find the requested value. - $f(x)=8 x+5 ; f(7)$

$f(x)=x^{2}-3$ and $g(x)=8 x+6$ ; (g of $)(x)$ .

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(4 r^{2}+\frac{45}{7} r-1\right) \div(7 r-1)$

Find the value of the expression. - $\frac{7 \times 10^{-3}}{28 \times 10^{2}}$

Combine terms. - $3 q^{-9}+10 q^{-9}-9 q^{-9}$

Choose the one alternative that best completes the statement or answers the question - $-9^{2}$

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

Find ( f(g)(x)f(g)(x)f(g)(x) for the given functions f(x)f(x)f(x) and g(x)g(x)g(x) . - f(x)=7x+6f(x)=7 x+6f(x)=7x+6 and g(x)=7x−6g(x)=7 x-6g(x)=7x−6

Find the result that a calculator will give for the stated problem. Write your answer using the usual scientific notation. -(7.2E17)/(3E-7)

Choose the one alternative that best completes the statement or answers the question. Divide - 18x8+21x6+24x43x6\frac{18 x^{8}+21 x^{6}+24 x^{4}}{3 x^{6}}3x618x8+21x6+24x4​

Express the number in standard notation. - 8.213×10−68.213 \times 10^{-6}8.213×10−6

Find the product - 4x3(5x−8)4 x^{3}(5 x-8)4x3(5x−8)

Apply the product rule for exponents, if possible. - g10⋅h8\mathrm{g}^{10} \cdot \mathrm{h}^{8}g10⋅h8

For what values, if any, of x(x≠0)x(x \neq 0)x(x=0) and nnn will x−nx^{-n}x−n be a negative number?

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - 66−1\frac{6}{6^{-1}}6−16​

Find the product - (p+6)2(\mathrm{p}+6)^{2}(p+6)2

Perform the indicated operations. - (4x−10)(x−1)(4 x-10)(x-1)(4x−10)(x−1)

The fact that 8?56=78 ? { 5 6 } = 78?56=7 and 7?56=87 ? { 5 6 } = 87?56=8 demonstrates a way to check division. Perform the following division, and then use the above property to check it.

Decide whether the expression has been simplified correctly. - (6b)2=6b2(6 b)^{2}=6 b^{2}(6b)2=6b2

Decide whether the expression has been simplified correctly. - x7⋅x6=x42x^{7} \cdot x^{6}=x^{42}x7⋅x6=x42

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - x5x17\frac{x^{5}}{x^{17}}x17x5​

For the polynomial function, find the requested value. - f(x)=8x+5;f(7)f(x)=8 x+5 ; f(7)f(x)=8x+5;f(7)

f(x)=x2−3f(x)=x^{2}-3f(x)=x2−3 and g(x)=8x+6g(x)=8 x+6g(x)=8x+6 ; (g of )(x))(x))(x) .

Choose the one alternative that best completes the statement or answers the question. Divide - (4r2+457r−1)÷(7r−1)\left(4 r^{2}+\frac{45}{7} r-1\right) \div(7 r-1)(4r2+745​r−1)÷(7r−1)

Find the value of the expression. - 7×10−328×102\frac{7 \times 10^{-3}}{28 \times 10^{2}}28×1027×10−3​

Combine terms. - 3q−9+10q−9−9q−93 q^{-9}+10 q^{-9}-9 q^{-9}3q−9+10q−9−9q−9

Choose the one alternative that best completes the statement or answers the question - −92-9^{2}−92

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

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=7 x+6$ and $g(x)=7 x-6$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{18 x^{8}+21 x^{6}+24 x^{4}}{3 x^{6}}$

Express the number in standard notation. - $8.213 \times 10^{-6}$

Find the product - $4 x^{3}(5 x-8)$

Apply the product rule for exponents, if possible. - $\mathrm{g}^{10} \cdot \mathrm{h}^{8}$

For what values, if any, of $x(x \neq 0)$ and $n$ will $x^{-n}$ be a negative number?

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{6}{6^{-1}}$

Find the product - $(\mathrm{p}+6)^{2}$

Perform the indicated operations. - $(4 x-10)(x-1)$

The fact that $8 ? { 5 6 } = 7$ and $7 ? { 5 6 } = 8$ demonstrates a way to check division. Perform the following division, and then use the above property to check it.

Decide whether the expression has been simplified correctly. - $(6 b)^{2}=6 b^{2}$

Decide whether the expression has been simplified correctly. - $x^{7} \cdot x^{6}=x^{42}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{5}}{x^{17}}$

For the polynomial function, find the requested value. - $f(x)=8 x+5 ; f(7)$

$f(x)=x^{2}-3$ and $g(x)=8 x+6$ ; (g of $)(x)$ .

Choose the one alternative that best completes the statement or answers the question. Divide - $\left(4 r^{2}+\frac{45}{7} r-1\right) \div(7 r-1)$

Find the value of the expression. - $\frac{7 \times 10^{-3}}{28 \times 10^{2}}$

Combine terms. - $3 q^{-9}+10 q^{-9}-9 q^{-9}$

Choose the one alternative that best completes the statement or answers the question - $-9^{2}$