Question 1

Express the number in scientific notation
-0.0000011313

Accepted Answer

A)  $1.1313 \times 10^{6}$ 
B)  $1.1313 \times 10^{-5}$ 
C)  $1.1313 \times 10^{-7}$ 
D)  $1.1313 \times 10^{-6}$ 
A)  $1.1313 \times 10^{6}$ 
B)  $1.1313 \times 10^{-5}$ 
C)  $1.1313 \times 10^{-7}$ 
D)  $1.1313 \times 10^{-6}$

Question 2

Express the number in scientific notation
-0.000000939012

Accepted Answer

A)  $9.39012 \times 10^{7}$ 
B)  $9.39012 \times 10^{-6}$ 
C)  $9.39012 \times 10^{6}$ 
D)  $9.39012 \times 10^{-7}$ 
A)  $9.39012 \times 10^{7}$ 
B)  $9.39012 \times 10^{-6}$ 
C)  $9.39012 \times 10^{6}$ 
D)  $9.39012 \times 10^{-7}$

Question 3

$(x+3 y)^{3}$

Accepted Answer

A)  $3(x+3 y)$ 
B)  $x^{3}+27 y^{3}$ 
C)  $x^{3}+9 x^{2} y+27 x y^{2}+27 y^{3}$ 
D)  $x^{3}+3 x^{2} y+6 x y+9 x y^{2}+18 y^{2}+27 y^{3}$ 
A)  $3(x+3 y)$ 
B)  $x^{3}+27 y^{3}$ 
C)  $x^{3}+9 x^{2} y+27 x y^{2}+27 y^{3}$ 
D)  $x^{3}+3 x^{2} y+6 x y+9 x y^{2}+18 y^{2}+27 y^{3}$

Question 4

Express the area of the figure as a polynomial in descending powers of the variable $x$.
-

Accepted Answer

A)  $2 x^{3}+17 x^{2}+11 x-1$ 
B)  $2 x^{3}-19 x^{2}+7 x+1$ 
C)  $2 x^{3}-17 x^{2}-11 x-1$ 
D)  $2 x^{3}+19 x^{2}+7 x-1$ 
A)  $2 x^{3}+17 x^{2}+11 x-1$ 
B)  $2 x^{3}-19 x^{2}+7 x+1$ 
C)  $2 x^{3}-17 x^{2}-11 x-1$ 
D)  $2 x^{3}+19 x^{2}+7 x-1$

Question 5

For the given pair of functions, find the requested function.
-If $f(x)=18 x^{3}-15 x^{2}-57 x-2$ and $g(x)=6 x+9$, find $\left(\frac{f}{g}\right)(4)$.

Accepted Answer

A)  $\frac{62}{3}$ 
B)  $\frac{1172}{33}$ 
C)  $\frac{652}{63}$ 
D)  0 
A)  $\frac{62}{3}$ 
B)  $\frac{1172}{33}$ 
C)  $\frac{652}{63}$ 
D)  0

Question 6

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$.
-$f(x)=x+7$ and $g(x)=8 x-9$

Accepted Answer

A)  $8 x-2$ 
B)  $7 x+16$ 
C)  $8 x+47$ 
D)  $9 x-2$ 
A)  $8 x-2$ 
B)  $7 x+16$ 
C)  $8 x+47$ 
D)  $9 x-2$

Question 7

Decide whether the expression has been simplified correctly.
-$(a b)^{3}=a b^{3}$

Accepted Answer

A) True 
 B)False

Question 8

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}$

Accepted Answer

A)  $\frac{81 x^{2}}{25 y^{14}}$ 
B)  $\frac{81 x^{2} y^{14}}{5}$ 
C)  $\frac{25 x^{3}}{9 y^{14}}$ 
D)  $-\frac{27 x}{25 y^{10}}$ 
A)  $\frac{81 x^{2}}{25 y^{14}}$ 
B)  $\frac{81 x^{2} y^{14}}{5}$ 
C)  $\frac{25 x^{3}}{9 y^{14}}$ 
D)  $-\frac{27 x}{25 y^{10}}$

Question 9

Find the product
-$(8 y+x)(8 y-x)$

Accepted Answer

A)  $64 y^{2}+16 x y-x^{2}$ 
B)  $64 y^{2}-x^{2}$ 
C)  $16 y^{2}-x^{2}$ 
D)  $64 y^{2}-16 x y-x^{2}$ 
A)  $64 y^{2}+16 x y-x^{2}$ 
B)  $64 y^{2}-x^{2}$ 
C)  $16 y^{2}-x^{2}$ 
D)  $64 y^{2}-16 x y-x^{2}$

Question 10

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

Accepted Answer

A)  $7^{7} \cdot 4^{7}$ 
B)  $7^{10} \cdot 4^{25}$ 
C)  $\frac{1}{7^{7} \cdot 4^{7}}$ 
D)  $\frac{1}{7^{10} \cdot 4^{25}}$ 
A)  $7^{7} \cdot 4^{7}$ 
B)  $7^{10} \cdot 4^{25}$ 
C)  $\frac{1}{7^{7} \cdot 4^{7}}$ 
D)  $\frac{1}{7^{10} \cdot 4^{25}}$

Question 11

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers.
-$\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}$

Accepted Answer

A)  $\frac{16 p^{2}}{q^{8}}$ 
B)  $\frac{16 q^{2}}{p^{-8}}$ 
C)  $\frac{p^{2}}{16 q^{-8}}$ 
D)  $\frac{16 p^{2}}{q^{-8}}$ 
A)  $\frac{16 p^{2}}{q^{8}}$ 
B)  $\frac{16 q^{2}}{p^{-8}}$ 
C)  $\frac{p^{2}}{16 q^{-8}}$ 
D)  $\frac{16 p^{2}}{q^{-8}}$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Divide
-$\frac{24 x^{9}-24 x^{6}}{-4 x^{9}}$

Accepted Answer

A)  $-6-24 x^{6}$ 
B)  $24 x^{9}+\frac{6}{x^{3}}$ 
C)  $-6+\frac{6}{x^{3}}$ 
D)  $-6+6 x^{3}$ 
A)  $-6-24 x^{6}$ 
B)  $24 x^{9}+\frac{6}{x^{3}}$ 
C)  $-6+\frac{6}{x^{3}}$ 
D)  $-6+6 x^{3}$

Question 13

Why is scientific notation used?

Accepted Answer

Scientific notation is used for several

Question 14

Add or subtract as indicated.
-$\left(8 a^{3}+6 a^{2}\right)+\left(4 a^{3}+5 a^{2}\right)$

Accepted Answer

A)  $12 a^{3}+11 a^{2}$ 
B)  $23 \mathrm{a}^{10}$ 
C)  $12 a^{6}+11 a^{4}$ 
D)  $23 a^{5}$ 
A)  $12 a^{3}+11 a^{2}$ 
B)  $23 \mathrm{a}^{10}$ 
C)  $12 a^{6}+11 a^{4}$ 
D)  $23 a^{5}$

Question 15

Evaluate the expression.
-$\left(\frac{5}{3}\right)^{-3}$

Accepted Answer

A)  $\frac{27}{125}$ 
B)  $\frac{125}{27}$ 
C)  $-\frac{27}{125}$ 
D)  $-\frac{125}{27}$ 
A)  $\frac{27}{125}$ 
B)  $\frac{125}{27}$ 
C)  $-\frac{27}{125}$ 
D)  $-\frac{125}{27}$

Question 16

$f(x)=x^{2}+4$ and $g(x)=2 x+7$; (g of)(5).

Accepted Answer

A)  51 
B)  65 
C)  36 
D)  293 
A)  51 
B)  65 
C)  36 
D)  293

Question 17

$f(x)=5 x^{2}-3 x-1$ and $g(x)=x-1 ;(f \circ g)(x)$.

Accepted Answer

A)  $5 x^{2}-13 x+7$ 
B)  $5 x^{2}-8 x+1$ 
C)  $5 x^{2}-13 x+1$ 
D)  $-13 x^{2}+5 x+7$ 
A)  $5 x^{2}-13 x+7$ 
B)  $5 x^{2}-8 x+1$ 
C)  $5 x^{2}-13 x+1$ 
D)  $-13 x^{2}+5 x+7$

Question 18

$(4 x+3)^{4}$

Accepted Answer

A)  $\left(16 x^{2}+12 x+9\right)^{4}$ 
B)  $768 x^{4}+2304 x^{3}+864 x^{2}+1296 x+81$ 
C)  $256 x^{4}+768 x^{3}+864 x^{2}+432 x+81$ 
D)  $256 x^{3}+768 x^{2}+864 x+432$ 
A)  $\left(16 x^{2}+12 x+9\right)^{4}$ 
B)  $768 x^{4}+2304 x^{3}+864 x^{2}+1296 x+81$ 
C)  $256 x^{4}+768 x^{3}+864 x^{2}+432 x+81$ 
D)  $256 x^{3}+768 x^{2}+864 x+432$

Question 19

In scientific notation, what is the smallest positive integer which can be multiplied by a power of $10 ?$

Accepted Answer

A)  1 
B)  -1 
C)  0 
D)  -9 
A)  1 
B)  -1 
C)  0 
D)  -9

Question 20

A manufacturer of medical supplies produces 1 -liter bags of saline solution. The cost to produce $x$ thousand bags of saline is given by the cost function $C(x)=1.6 x^{2}-5.7 x+2.9$, where $C$ is the cost in thousands of dollars. Find the cost to produce 3000 bags of saline.

Accepted Answer

A)  $\$ 24,800$ 
B)  $\$ 200$ 
C)  $\$ 34,400$ 
D)  $\$ 0.20$ 
A)  $\$ 24,800$ 
B)  $\$ 200$ 
C)  $\$ 34,400$ 
D)  $\$ 0.20$

Express the number in scientific notation -0.0000011313

Express the number in scientific notation -0.000000939012

$(x+3 y)^{3}$

Express the area of the figure as a polynomial in descending powers of the variable $x$ . -

For the given pair of functions, find the requested function. -If $f(x)=18 x^{3}-15 x^{2}-57 x-2$ and $g(x)=6 x+9$ , find $\left(\frac{f}{g}\right)(4)$ .

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=x+7$ and $g(x)=8 x-9$

Decide whether the expression has been simplified correctly. - $(a b)^{3}=a b^{3}$

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}$

Find the product - $(8 y+x)(8 y-x)$

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

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{24 x^{9}-24 x^{6}}{-4 x^{9}}$

Why is scientific notation used?

Add or subtract as indicated. - $\left(8 a^{3}+6 a^{2}\right)+\left(4 a^{3}+5 a^{2}\right)$

Evaluate the expression. - $\left(\frac{5}{3}\right)^{-3}$

$f(x)=x^{2}+4$ and $g(x)=2 x+7$ ; (g of)(5).

$f(x)=5 x^{2}-3 x-1$ and $g(x)=x-1 ;(f \circ g)(x)$ .

$(4 x+3)^{4}$

In scientific notation, what is the smallest positive integer which can be multiplied by a power of $10 ?$

A manufacturer of medical supplies produces 1 -liter bags of saline solution. The cost to produce $x$ thousand bags of saline is given by the cost function $C(x)=1.6 x^{2}-5.7 x+2.9$ , where $C$ is the cost in thousands of dollars. Find the cost to produce 3000 bags of saline.

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

Express the number in scientific notation -0.0000011313

Express the number in scientific notation -0.000000939012

(x+3y)3(x+3 y)^{3}(x+3y)3

Express the area of the figure as a polynomial in descending powers of the variable xxx . -

For the given pair of functions, find the requested function. -If f(x)=18x3−15x2−57x−2f(x)=18 x^{3}-15 x^{2}-57 x-2f(x)=18x3−15x2−57x−2 and g(x)=6x+9g(x)=6 x+9g(x)=6x+9 , find (fg)(4)\left(\frac{f}{g}\right)(4)(gf​)(4) .

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)=x+7f(x)=x+7f(x)=x+7 and g(x)=8x−9g(x)=8 x-9g(x)=8x−9

Decide whether the expression has been simplified correctly. - (ab)3=ab3(a b)^{3}=a b^{3}(ab)3=ab3

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - (9x2y2)3(15x2y−4)−2\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}(y29x2​)3(y−415x2​)−2

Find the product - (8y+x)(8y−x)(8 y+x)(8 y-x)(8y+x)(8y−x)

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - (72⋅45)−5\left(7^{2} \cdot 4^{5}\right)^{-5}(72⋅45)−5

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - (4p3q6)−2(16p4q2)2\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}(4p3q6)−2(16p4q2)2

Choose the one alternative that best completes the statement or answers the question. Divide - 24x9−24x6−4x9\frac{24 x^{9}-24 x^{6}}{-4 x^{9}}−4x924x9−24x6​

Why is scientific notation used?

Add or subtract as indicated. - (8a3+6a2)+(4a3+5a2)\left(8 a^{3}+6 a^{2}\right)+\left(4 a^{3}+5 a^{2}\right)(8a3+6a2)+(4a3+5a2)

Evaluate the expression. - (53)−3\left(\frac{5}{3}\right)^{-3}(35​)−3

f(x)=x2+4f(x)=x^{2}+4f(x)=x2+4 and g(x)=2x+7g(x)=2 x+7g(x)=2x+7 ; (g of)(5).

f(x)=5x2−3x−1f(x)=5 x^{2}-3 x-1f(x)=5x2−3x−1 and g(x)=x−1;(f∘g)(x)g(x)=x-1 ;(f \circ g)(x)g(x)=x−1;(f∘g)(x) .

(4x+3)4(4 x+3)^{4}(4x+3)4

In scientific notation, what is the smallest positive integer which can be multiplied by a power of 10?10 ?10?

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

$(x+3 y)^{3}$

Express the area of the figure as a polynomial in descending powers of the variable $x$ . -

For the given pair of functions, find the requested function. -If $f(x)=18 x^{3}-15 x^{2}-57 x-2$ and $g(x)=6 x+9$ , find $\left(\frac{f}{g}\right)(4)$ .

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=x+7$ and $g(x)=8 x-9$

Decide whether the expression has been simplified correctly. - $(a b)^{3}=a b^{3}$

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(\frac{9 x^{2}}{y^{2}}\right)^{3}\left(\frac{15 x^{2}}{y^{-4}}\right)^{-2}$

Find the product - $(8 y+x)(8 y-x)$

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

Simplify. Write the answer with only positive exponents. Assume that all variables represent nonzero real numbers. - $\left(4 \mathrm{p}^{3} \mathrm{q}^{6}\right)^{-2}\left(16 \mathrm{p}^{4} \mathrm{q}^{2}\right)^{2}$

Choose the one alternative that best completes the statement or answers the question. Divide - $\frac{24 x^{9}-24 x^{6}}{-4 x^{9}}$

Add or subtract as indicated. - $\left(8 a^{3}+6 a^{2}\right)+\left(4 a^{3}+5 a^{2}\right)$

Evaluate the expression. - $\left(\frac{5}{3}\right)^{-3}$

$f(x)=x^{2}+4$ and $g(x)=2 x+7$ ; (g of)(5).

$f(x)=5 x^{2}-3 x-1$ and $g(x)=x-1 ;(f \circ g)(x)$ .

$(4 x+3)^{4}$

In scientific notation, what is the smallest positive integer which can be multiplied by a power of $10 ?$