Question 1

Write in radical form. Assume all variables represent positive real numbers.
-$$( m n ) ^ { 1 / 5 }$$

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 5 ] { m n } }$ 
B)  $( \sqrt { \mathrm { mn } } ) ^ { 5 }$ 
C)  $\sqrt [ 5 ] { \mathrm { mn } }$ 
D)  $( \mathrm { mn } ) ^ { - 5 }$ 
A)  $\frac { 1 } { \sqrt [ 5 ] { m n } }$ 
B)  $( \sqrt { \mathrm { mn } } ) ^ { 5 }$ 
C)  $\sqrt [ 5 ] { \mathrm { mn } }$ 
D)  $( \mathrm { mn } ) ^ { - 5 }$

Question 2

Find the product.
-$$( w - 6 ) ^ { 2 }$$

Accepted Answer

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

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$$8 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$$

Accepted Answer

A)  $4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
B)  $4 x \sqrt [ 4 ] { x ^ { 7 } }$ 
C)  $8 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
D)  $12 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
A)  $4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
B)  $4 x \sqrt [ 4 ] { x ^ { 7 } }$ 
C)  $8 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
D)  $12 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$

Question 4

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$, and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$. $\{ 0,7,11 \} \subseteq \mathrm { C }$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 5

Evaluate the expression.
-$- | - 2 |$

Accepted Answer

A)  2 
B)  $- 2$ 
C)  0 
D)  $\pm 2$ 
A)  2 
B)  $- 2$ 
C)  0 
D)  $\pm 2$

Question 6

Factor out the greatest common factor. Simplify the factors, if possible.
-$$4 x ( 5 x + 3 ) - 3 ( 5 x + 3 )$$

Accepted Answer

A)  $( 4 x - 3 ) ( 5 x + 3 )$ 
B)  $( 20 x - 3 ) ( x + 3 )$ 
C)  $( 4 x + 3 ) ( 5 x - 3 )$ 
D)  $( 20 x + 3 ) ( x - 3 )$ 
A)  $( 4 x - 3 ) ( 5 x + 3 )$ 
B)  $( 20 x - 3 ) ( x + 3 )$ 
C)  $( 4 x + 3 ) ( 5 x - 3 )$ 
D)  $( 20 x + 3 ) ( x - 3 )$

Question 7

Find the product. Assume variables represent positive real numbers.
-$$\mathrm { y } ^ { 1 / 3 } \left( \mathrm { y } ^ { 4 / 9 } - 6 \mathrm { y } ^ { 2 / 9 } \right)$$

Accepted Answer

A)  $y ^ { 7 / 9 } - 6 y ^ { 5 / 9 }$ 
B)  $y ^ { 3 / 4 } - 6 y ^ { 3 / 2 }$ 
C)  $y ^ { 4 / 27 } - 6 y ^ { 2 / 27 }$ 
D)  $y ^ { - 1 / 9 } - 6 y ^ { 1 / 9 }$ 
A)  $y ^ { 7 / 9 } - 6 y ^ { 5 / 9 }$ 
B)  $y ^ { 3 / 4 } - 6 y ^ { 3 / 2 }$ 
C)  $y ^ { 4 / 27 } - 6 y ^ { 2 / 27 }$ 
D)  $y ^ { - 1 / 9 } - 6 y ^ { 1 / 9 }$

Question 8

Find the product.
-$$( - 5 x + 3 y ) ( 2 x + 12 y + 1 )$$

Accepted Answer

A)  $- 10 x ^ { 2 } - 54 x y - 54 y ^ { 2 }$ 
B)  $- 10 x ^ { 2 } + 6 x y - 5 x + 36 y ^ { 2 } + 3 y$ 
C)  $- 10 x ^ { 2 } - 54 x y - 5 x + 36 y ^ { 2 } + 3 y$ 
D)  $- 10 x ^ { 2 } - 60 x y - 5 x + 36 y ^ { 2 }$ 
A)  $- 10 x ^ { 2 } - 54 x y - 54 y ^ { 2 }$ 
B)  $- 10 x ^ { 2 } + 6 x y - 5 x + 36 y ^ { 2 } + 3 y$ 
C)  $- 10 x ^ { 2 } - 54 x y - 5 x + 36 y ^ { 2 } + 3 y$ 
D)  $- 10 x ^ { 2 } - 60 x y - 5 x + 36 y ^ { 2 }$

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 500 } { 27 } }$

Accepted Answer

A)  $\frac { 10 \sqrt { 15 } } { 9 }$ 
B)  $\frac { 5 } { \sqrt { 27 } }$ 
C)  $\frac { 3 } { 5 }$ 
D)  $\frac { \sqrt { 4 } } { 3 }$ 
A)  $\frac { 10 \sqrt { 15 } } { 9 }$ 
B)  $\frac { 5 } { \sqrt { 27 } }$ 
C)  $\frac { 3 } { 5 }$ 
D)  $\frac { \sqrt { 4 } } { 3 }$

Question 10

Find the product.
-$$2 x ( 3 x - 1 ) ( 6 x + 9 )$$

Accepted Answer

A)  $36 x ^ { 3 } + 42 x ^ { 2 } - 18 x$ 
B)  $32 x ^ { 3 } + 44 x ^ { 2 } - 16 x$ 
C)  $34 x ^ { 2 } + 43 x - 18$ 
D)  $18 x ^ { 3 } + 21 x ^ { 2 } - 9 x$ 
A)  $36 x ^ { 3 } + 42 x ^ { 2 } - 18 x$ 
B)  $32 x ^ { 3 } + 44 x ^ { 2 } - 16 x$ 
C)  $34 x ^ { 2 } + 43 x - 18$ 
D)  $18 x ^ { 3 } + 21 x ^ { 2 } - 9 x$

Question 11

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$x ^ { 2 } y < 0$$

Accepted Answer

A)  y must be negative. 
B)  x and y must be negative. 
C)  x and y have different signs. 
D)  x must be negative. 
A)  y must be negative. 
B)  x and y must be negative. 
C)  x and y have different signs. 
D)  x must be negative.

Question 12

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-0_____{ 1,2,3,4,5,6 }

Accepted Answer

A)  $\in$ 
B)  $\notin$ 
A)  $\in$ 
B)  $\notin$

Question 13

Evaluate the expression.
-$\frac { 8 \cdot 5 - 6 - ( - 6 + 1 ) } { 8 \cdot 3 - 8 }$

Accepted Answer

A)  $- \frac { 1 } { 16 }$ 
B)  $\frac { 39 } { 16 }$ 
C)  $- \frac { 39 } { 40 }$ 
D)  $\frac { 3 } { 40 }$ 
A)  $- \frac { 1 } { 16 }$ 
B)  $\frac { 39 } { 16 }$ 
C)  $- \frac { 39 } { 40 }$ 
D)  $\frac { 3 } { 40 }$

Question 14

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$$\frac { 1 } { 4 } ( 16 y + 16 x + 8 z )$$

Accepted Answer

A)  4y + 4x + 2z 
B)  4y + 4x - 2z 
C)  4y - 4x + 2z 
D)  4y - 4x - 2z 
A)  4y + 4x + 2z 
B)  4y + 4x - 2z 
C)  4y - 4x + 2z 
D)  4y - 4x - 2z

Question 15

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }$$

Accepted Answer

A)  $- 3 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
B)  $3 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 3 } }$ 
C)  $3 a b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
D)  not a real number 
A)  $- 3 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
B)  $3 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 3 } }$ 
C)  $3 a b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
D)  not a real number

Question 16

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 3,4,5,6,7,8 \} , \mathrm { B } = \{ 5,7,9 \} , \mathrm { C } = \{ 3,4,6,8 \} , \mathrm { D } = \{ 3,8 \}$, and $\mathrm { U } = \{ 3,4,5,6,7,8,9 \}$
$\mathrm { C } \subseteq \mathrm { A }$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 17

Tell whether the statement is true or false.
-$$\{ 3,5,6,8 \} \cap \varnothing = \{ 3,5,6,8 \}$$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 18

Factor, using the given factor. Assume all variables represent positive real numbers.
-$$( q + 5 ) ^ { - 3 / 5 } + ( q + 5 ) ^ { - 1 / 5 } + ( q + 5 ) ^ { 1 / 5 } ; \quad ( q + 5 ) ^ { - 3 / 5 }$$

Accepted Answer

A)  $( \mathrm { q } + 5 ) ^ { - 3 / 5 } \left[ 1 + ( \mathrm { q } + 5 ) ^ { 2 / 5 } + ( \mathrm { q } + 5 ) ^ { 4 / 5 } \right]$ 
B)  $( q + 5 ) ^ { - 3 / 5 } \left[ 1 + ( q + 5 ) ^ { 1 / 5 } + ( q + 5 ) ^ { 3 / 5 } \right]$ 
C)  $( q + 5 ) ^ { - 3 / 5 } \left[ 1 + ( q + 5 ) ^ { - 2 / 5 } + ( q + 5 ) ^ { - 4 / 5 } \right]$ 
D)  $( q + 5 ) ^ { - 3 / 5 } \left[ 1 + ( q + 5 ) ^ { 4 / 5 } + ( q + 5 ) ^ { 6 / 5 } \right]$ 
A)  $( \mathrm { q } + 5 ) ^ { - 3 / 5 } \left[ 1 + ( \mathrm { q } + 5 ) ^ { 2 / 5 } + ( \mathrm { q } + 5 ) ^ { 4 / 5 } \right]$ 
B)  $( q + 5 ) ^ { - 3 / 5 } \left[ 1 + ( q + 5 ) ^ { 1 / 5 } + ( q + 5 ) ^ { 3 / 5 } \right]$ 
C)  $( q + 5 ) ^ { - 3 / 5 } \left[ 1 + ( q + 5 ) ^ { - 2 / 5 } + ( q + 5 ) ^ { - 4 / 5 } \right]$ 
D)  $( q + 5 ) ^ { - 3 / 5 } \left[ 1 + ( q + 5 ) ^ { 4 / 5 } + ( q + 5 ) ^ { 6 / 5 } \right]$

Question 19

Use set notation, and list all the elements of the set.
-$\{ 12,13,14 , \ldots , 18 \}$

Accepted Answer

A)  $\{ 12,13,14,15,16,17,18 \}$ 
B)  $\{ 12,14,16,18 \}$ 
C)  $\{ 12,13,15,17,18 \}$ 
D)  $\{ 12,13,14,15,16,17,18,19 \}$ 
A)  $\{ 12,13,14,15,16,17,18 \}$ 
B)  $\{ 12,14,16,18 \}$ 
C)  $\{ 12,13,15,17,18 \}$ 
D)  $\{ 12,13,14,15,16,17,18,19 \}$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- x ^ { - 4 }$

Accepted Answer

A)  $- 4 x$ 
B)  $- \frac { 1 } { x ^ { 4 } }$ 
C)  $4 \mathrm { x }$ 
D)  $\frac { 1 } { x ^ { 4 } }$ 
A)  $- 4 x$ 
B)  $- \frac { 1 } { x ^ { 4 } }$ 
C)  $4 \mathrm { x }$ 
D)  $\frac { 1 } { x ^ { 4 } }$

Write in radical form. Assume all variables represent positive real numbers. - $( m n ) ^ { 1 / 5 }$

Find the product. - $( w - 6 ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $8 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$ , and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$ . $\{ 0,7,11 \} \subseteq \mathrm { C }$

Evaluate the expression. - $- | - 2 |$

Factor out the greatest common factor. Simplify the factors, if possible. - $4 x ( 5 x + 3 ) - 3 ( 5 x + 3 )$

Find the product. Assume variables represent positive real numbers. - $\mathrm { y } ^ { 1 / 3 } \left( \mathrm { y } ^ { 4 / 9 } - 6 \mathrm { y } ^ { 2 / 9 } \right)$

Find the product. - $( - 5 x + 3 y ) ( 2 x + 12 y + 1 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 500 } { 27 } }$

Find the product. - $2 x ( 3 x - 1 ) ( 6 x + 9 )$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x ^ { 2 } y < 0$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -0_____{ 1,2,3,4,5,6 }

Evaluate the expression. - $\frac { 8 \cdot 5 - 6 - ( - 6 + 1 ) } { 8 \cdot 3 - 8 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { 4 } ( 16 y + 16 x + 8 z )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 3,4,5,6,7,8 \} , \mathrm { B } = \{ 5,7,9 \} , \mathrm { C } = \{ 3,4,6,8 \} , \mathrm { D } = \{ 3,8 \}$ , and $\mathrm { U } = \{ 3,4,5,6,7,8,9 \}$ $\mathrm { C } \subseteq \mathrm { A }$

Tell whether the statement is true or false. - $\{ 3,5,6,8 \} \cap \varnothing = \{ 3,5,6,8 \}$

Factor, using the given factor. Assume all variables represent positive real numbers. - $( q + 5 ) ^ { - 3 / 5 } + ( q + 5 ) ^ { - 1 / 5 } + ( q + 5 ) ^ { 1 / 5 } ; \quad ( q + 5 ) ^ { - 3 / 5 }$

Use set notation, and list all the elements of the set. - $\{ 12,13,14 , \ldots , 18 \}$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- x ^ { - 4 }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 12: Review of Basic Concepts

Write in radical form. Assume all variables represent positive real numbers. - (mn)1/5( m n ) ^ { 1 / 5 }(mn)1/5

Find the product. - (w−6)2( w - 6 ) ^ { 2 }(w−6)2

Simplify the expression. Assume all variables represent positive real numbers. - 8x74−4xx348 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }84x7​−4x4x3​

Evaluate the expression. - −∣−2∣- | - 2 |−∣−2∣

Factor out the greatest common factor. Simplify the factors, if possible. - 4x(5x+3)−3(5x+3)4 x ( 5 x + 3 ) - 3 ( 5 x + 3 )4x(5x+3)−3(5x+3)

Find the product. Assume variables represent positive real numbers. - y1/3(y4/9−6y2/9)\mathrm { y } ^ { 1 / 3 } \left( \mathrm { y } ^ { 4 / 9 } - 6 \mathrm { y } ^ { 2 / 9 } \right)y1/3(y4/9−6y2/9)

Find the product. - (−5x+3y)(2x+12y+1)( - 5 x + 3 y ) ( 2 x + 12 y + 1 )(−5x+3y)(2x+12y+1)

Simplify the expression. Assume all variables represent positive real numbers. - 50027\sqrt { \frac { 500 } { 27 } }27500​​

Find the product. - 2x(3x−1)(6x+9)2 x ( 3 x - 1 ) ( 6 x + 9 )2x(3x−1)(6x+9)

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - x2y<0x ^ { 2 } y < 0x2y<0

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -0_____{ 1,2,3,4,5,6 }

Evaluate the expression. - 8⋅5−6−(−6+1)8⋅3−8\frac { 8 \cdot 5 - 6 - ( - 6 + 1 ) } { 8 \cdot 3 - 8 }8⋅3−88⋅5−6−(−6+1)​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 14(16y+16x+8z)\frac { 1 } { 4 } ( 16 y + 16 x + 8 z )41​(16y+16x+8z)

Simplify the expression. Assume all variables represent positive real numbers. - −27a8b53\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }3−27a8b5​

Tell whether the statement is true or false. - {3,5,6,8}∩∅={3,5,6,8}\{ 3,5,6,8 \} \cap \varnothing = \{ 3,5,6,8 \}{3,5,6,8}∩∅={3,5,6,8}

Factor, using the given factor. Assume all variables represent positive real numbers. - (q+5)−3/5+(q+5)−1/5+(q+5)1/5;(q+5)−3/5( q + 5 ) ^ { - 3 / 5 } + ( q + 5 ) ^ { - 1 / 5 } + ( q + 5 ) ^ { 1 / 5 } ; \quad ( q + 5 ) ^ { - 3 / 5 }(q+5)−3/5+(q+5)−1/5+(q+5)1/5;(q+5)−3/5

Use set notation, and list all the elements of the set. - {12,13,14,…,18}\{ 12,13,14 , \ldots , 18 \}{12,13,14,…,18}

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −x−4- x ^ { - 4 }−x−4

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Write in radical form. Assume all variables represent positive real numbers. - $( m n ) ^ { 1 / 5 }$

Find the product. - $( w - 6 ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $8 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Evaluate the expression. - $- | - 2 |$

Factor out the greatest common factor. Simplify the factors, if possible. - $4 x ( 5 x + 3 ) - 3 ( 5 x + 3 )$

Find the product. Assume variables represent positive real numbers. - $\mathrm { y } ^ { 1 / 3 } \left( \mathrm { y } ^ { 4 / 9 } - 6 \mathrm { y } ^ { 2 / 9 } \right)$

Find the product. - $( - 5 x + 3 y ) ( 2 x + 12 y + 1 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 500 } { 27 } }$

Find the product. - $2 x ( 3 x - 1 ) ( 6 x + 9 )$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x ^ { 2 } y < 0$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -0_____{ 1,2,3,4,5,6 }

Evaluate the expression. - $\frac { 8 \cdot 5 - 6 - ( - 6 + 1 ) } { 8 \cdot 3 - 8 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { 4 } ( 16 y + 16 x + 8 z )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }$

Tell whether the statement is true or false. - $\{ 3,5,6,8 \} \cap \varnothing = \{ 3,5,6,8 \}$

Factor, using the given factor. Assume all variables represent positive real numbers. - $( q + 5 ) ^ { - 3 / 5 } + ( q + 5 ) ^ { - 1 / 5 } + ( q + 5 ) ^ { 1 / 5 } ; \quad ( q + 5 ) ^ { - 3 / 5 }$

Use set notation, and list all the elements of the set. - $\{ 12,13,14 , \ldots , 18 \}$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- x ^ { - 4 }$