Question 1

Evaluate the expression.
-$$\left( \frac { 1 } { 64 } \right) ^ { 7 / 3 }$$

Accepted Answer

A)  $- 16,384$ 
B)  $\frac { 1 } { 16,384 }$ 
C)  not a real number 
D)  $- \frac { 448 } { 3 }$ 
A)  $- 16,384$ 
B)  $\frac { 1 } { 16,384 }$ 
C)  not a real number 
D)  $- \frac { 448 } { 3 }$

Question 2

Factor by any method.
-$$125 a ^ { 3 } - 64 b ^ { 3 }$$

Accepted Answer

A)  $( 125 a - 4 b ) \left( a ^ { 2 } + 20 a b + 16 b ^ { 2 } \right)$ 
B)  $( 5 a - 4 b ) \left( 25 a ^ { 2 } + 20 a b + 16 b ^ { 2 } \right)$ 
C)  $( 5 a - 4 b ) \left( 25 a ^ { 2 } + 16 b ^ { 2 } \right)$ 
D)  $\left( 5 a + 4 b ^ { 2 } \right) \left( 25 a ^ { 2 } - 20 a b + 16 b ^ { 2 } \right)$ 
A)  $( 125 a - 4 b ) \left( a ^ { 2 } + 20 a b + 16 b ^ { 2 } \right)$ 
B)  $( 5 a - 4 b ) \left( 25 a ^ { 2 } + 20 a b + 16 b ^ { 2 } \right)$ 
C)  $( 5 a - 4 b ) \left( 25 a ^ { 2 } + 16 b ^ { 2 } \right)$ 
D)  $\left( 5 a + 4 b ^ { 2 } \right) \left( 25 a ^ { 2 } - 20 a b + 16 b ^ { 2 } \right)$

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }$

Accepted Answer

A)  3 
B)  27 
C)  $3 \sqrt [ 3 ] { 3 }$ 
D)  9 
A)  3 
B)  27 
C)  $3 \sqrt [ 3 ] { 3 }$ 
D)  9

Question 4

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { 18 } } { x ^ { 4 } }$$

Accepted Answer

A)  $x ^ { 14 }$ 
B)  $x ^ { 22 }$ 
C)  $- \mathrm { x } ^ { 14 }$ 
D)  $\frac { 1 } { x ^ { 14 } }$ 
A)  $x ^ { 14 }$ 
B)  $x ^ { 22 }$ 
C)  $- \mathrm { x } ^ { 14 }$ 
D)  $\frac { 1 } { x ^ { 14 } }$

Question 5

Find the product or quotient.
-$$\frac { k ^ { 2 } + 6 k + 9 } { k ^ { 2 } + 11 k + 24 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 11 k + 24 }$$

Accepted Answer

A)  $\frac { k ^ { 2 } + 8 k } { k + 8 }$ 
B)  $\frac { 1 } { k + 8 }$ 
C)  $\frac { \mathrm { k } } { \mathrm { k } + 8 }$ 
D)  $\frac { \mathrm { k } } { \mathrm { k } ^ { 2 } + 11 \mathrm { k } + 24 }$ 
A)  $\frac { k ^ { 2 } + 8 k } { k + 8 }$ 
B)  $\frac { 1 } { k + 8 }$ 
C)  $\frac { \mathrm { k } } { \mathrm { k } + 8 }$ 
D)  $\frac { \mathrm { k } } { \mathrm { k } ^ { 2 } + 11 \mathrm { k } + 24 }$

Question 6

Write in radical form. Assume all variables represent positive real numbers.
-$( - 6 x ) ^ { 1 / 5 }$

Accepted Answer

A)  $\sqrt { - \frac { 6 x } { 5 } }$ 
B)  $\sqrt [ 1 / 5 ] { - 6 x }$ 
C)  $\frac { 1 } { \sqrt [ 5 ] { - 6 x } }$ 
D)  $\sqrt [ 5 ] { - 6 x }$ 
A)  $\sqrt { - \frac { 6 x } { 5 } }$ 
B)  $\sqrt [ 1 / 5 ] { - 6 x }$ 
C)  $\frac { 1 } { \sqrt [ 5 ] { - 6 x } }$ 
D)  $\sqrt [ 5 ] { - 6 x }$

Question 7

Tell whether the statement is true or false.
-$$5 \in \{ 3,43,5,6 \}$$

Accepted Answer

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

Question 8

Evaluate the expression.
-$$- \left| \frac { 8 } { 5 } \right|$$

Accepted Answer

A)  $- \frac { 8 } { 5 }$ 
B)  0 
C)  $\frac { 8 } { 5 }$ 
D)  $\pm \frac { 8 } { 5 }$ 
A)  $- \frac { 8 } { 5 }$ 
B)  0 
C)  $\frac { 8 } { 5 }$ 
D)  $\pm \frac { 8 } { 5 }$

Question 9

Determine which property of absolute value justifies the statement.
-$$| x | \geq 0$$

Accepted Answer

A)  Property 1: the absolute value of a number is greater than 0 . 
B)  Property 5: the triangle inequality 
C)  Property 1: the absolute value of a number is positive or 0 . 
D)  Property 1: the absolute value of a number is positive. 
A)  Property 1: the absolute value of a number is greater than 0 . 
B)  Property 5: the triangle inequality 
C)  Property 1: the absolute value of a number is positive or 0 . 
D)  Property 1: the absolute value of a number is positive.

Question 10

Write in exponential form. Assume all variables are positive real numbers.
-$\sqrt [ 3 ] { \mathrm { x } ^ { 5 } }$

Accepted Answer

A)  $5 x ^ { 3 }$ 
B)  $x ^ { 3 / 5 }$ 
C)  $3 x ^ { 5 }$ 
D)  $x ^ { 5 / 3 }$ 
A)  $5 x ^ { 3 }$ 
B)  $x ^ { 3 / 5 }$ 
C)  $3 x ^ { 5 }$ 
D)  $x ^ { 5 / 3 }$

Question 11

Factor by any method.
-$$b ^ { 6 } - 64 a ^ { 6 }$$

Accepted Answer

A)  $\left( b ^ { 2 } - 4 a ^ { 2 } \right) \left( b ^ { 4 } + 4 b ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
B)  $( b + 2 a ) ( b - 2 a ) \left( b ^ { 4 } + 4 b ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
C)  $\left( b ^ { 3 } + 8 a ^ { 3 } \right) \left( b ^ { 3 } - 8 a ^ { 3 } \right)$ 
D)  $( b + 2 a ) ( b - 2 a ) \left( b ^ { 2 } + 2 b a + 4 a ^ { 2 } \right) \left( b ^ { 2 } - 2 b a + 4 a ^ { 2 } \right)$ 
A)  $\left( b ^ { 2 } - 4 a ^ { 2 } \right) \left( b ^ { 4 } + 4 b ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
B)  $( b + 2 a ) ( b - 2 a ) \left( b ^ { 4 } + 4 b ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
C)  $\left( b ^ { 3 } + 8 a ^ { 3 } \right) \left( b ^ { 3 } - 8 a ^ { 3 } \right)$ 
D)  $( b + 2 a ) ( b - 2 a ) \left( b ^ { 2 } + 2 b a + 4 a ^ { 2 } \right) \left( b ^ { 2 } - 2 b a + 4 a ^ { 2 } \right)$

Question 12

Find the product.
-$$( - 8 a - 9 b ) ( 9 a + 8 b )$$

Accepted Answer

A)  $- 72 a ^ { 2 } - 145 a b - 72 b ^ { 2 }$ 
B)  $- 72 a ^ { 2 } + 145 a b - 72 b ^ { 2 }$ 
C)  $- 72 a ^ { 2 } + 17 a b - 72 b ^ { 2 }$ 
D)  $- 72 a ^ { 2 } - 72 b ^ { 2 }$ 
A)  $- 72 a ^ { 2 } - 145 a b - 72 b ^ { 2 }$ 
B)  $- 72 a ^ { 2 } + 145 a b - 72 b ^ { 2 }$ 
C)  $- 72 a ^ { 2 } + 17 a b - 72 b ^ { 2 }$ 
D)  $- 72 a ^ { 2 } - 72 b ^ { 2 }$

Question 13

Solve the problem.
-Find all values of $b$ that will make the polynomial a perfect square trinomial. $25 x ^ { 2 } + 40 x + b$

Accepted Answer

A)  80 
B)  4 
C)  16 
D)  $4 , - 4$ 
A)  80 
B)  4 
C)  16 
D)  $4 , - 4$

Question 14

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { x ^ { - 4 } y ^ { 8 } } { x ^ { - 2 } y ^ { 5 } }$

Accepted Answer

A)  $\frac { x ^ { 2 } } { y ^ { 3 } }$ 
B)  $\frac { x ^ { 3 } } { y ^ { 4 } }$ 
C)  $\frac { y ^ { 3 } } { x ^ { 2 } }$ 
D)  $\frac { y ^ { 4 } } { x ^ { 3 } }$ 
A)  $\frac { x ^ { 2 } } { y ^ { 3 } }$ 
B)  $\frac { x ^ { 3 } } { y ^ { 4 } }$ 
C)  $\frac { y ^ { 3 } } { x ^ { 2 } }$ 
D)  $\frac { y ^ { 4 } } { x ^ { 3 } }$

Question 15

Find the product.
-$$( n + 11 ) ^ { 2 }$$

Accepted Answer

A)  $n + 121$ 
B)  $n ^ { 2 } + 22 n + 121$ 
C)  $121 \mathrm { n } ^ { 2 } + 22 \mathrm { n } + 121$ 
D)  $\mathrm { n } ^ { 2 } + 121$ 
A)  $n + 121$ 
B)  $n ^ { 2 } + 22 n + 121$ 
C)  $121 \mathrm { n } ^ { 2 } + 22 \mathrm { n } + 121$ 
D)  $\mathrm { n } ^ { 2 } + 121$

Question 16

Factor, using the given factor. Assume all variables represent positive real numbers.
-$8 m ^ { 3 / 4 } - 3 m - 1 / 2 ; \quad m ^ { - 1 / 2 }$

Accepted Answer

A)  $3 m ^ { - 1 / 4 } \left( 8 m ^ { 5 / 4 } - 1 \right)$ 
B)  $m ^ { - 1 / 2 } \left( 8 m ^ { 3 / 4 } + 3 \right)$ 
C)  $m ^ { - 1 / 2 } \left( 8 m ^ { 5 / 4 } - 3 \right)$ 
D)  $m - 1 / 2 \left( 24 m ^ { 5 / 4 } - 8 \right)$ 
A)  $3 m ^ { - 1 / 4 } \left( 8 m ^ { 5 / 4 } - 1 \right)$ 
B)  $m ^ { - 1 / 2 } \left( 8 m ^ { 3 / 4 } + 3 \right)$ 
C)  $m ^ { - 1 / 2 } \left( 8 m ^ { 5 / 4 } - 3 \right)$ 
D)  $m - 1 / 2 \left( 24 m ^ { 5 / 4 } - 8 \right)$

Question 17

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 5 ) ^ { - 2 }$

Accepted Answer

A)  $- \frac { 1 } { 25 }$ 
B)  25 
C)  $\frac { 1 } { 25 }$ 
D)  $- 25$ 
A)  $- \frac { 1 } { 25 }$ 
B)  25 
C)  $\frac { 1 } { 25 }$ 
D)  $- 25$

Question 18

Solve the problem.
-The length of the diagonal of a box is given by $\mathrm { D } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$ where $\mathrm { L } , \mathrm { W }$, and $\mathrm { H }$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $4 \mathrm { ft }$ long, $3 \mathrm { ft }$ high, and $2 \mathrm { ft }$ wide. Give the exact value.

Accepted Answer

A)  $9 \mathrm { ft }$ 
B)  $2 \sqrt { 6 } \mathrm { ft }$ 
C)  $\sqrt { 29 } \mathrm { ft }$ 
D)  $24 \mathrm { ft }$ 
A)  $9 \mathrm { ft }$ 
B)  $2 \sqrt { 6 } \mathrm { ft }$ 
C)  $\sqrt { 29 } \mathrm { ft }$ 
D)  $24 \mathrm { ft }$

Question 19

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { \left( x ^ { 2 } + 1 \right) ^ { 4 } ( 2 x ) - x ^ { 2 } ( 4 ) \left( x ^ { 2 } + 1 \right) ^ { 3 } ( 2 x ) } { \left( x ^ { 2 } + 1 \right) ^ { 8 } }$$

Accepted Answer

A)  $\frac { ( 2 x ) \left( 1 + 5 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
B)  $\frac { ( 2 x ) \left( 1 - 3 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
C)  $\frac { ( 2 x ) \left( 1 + 3 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
D)  $\frac { ( 2 x ) \left( 1 - 5 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
A)  $\frac { ( 2 x ) \left( 1 + 5 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
B)  $\frac { ( 2 x ) \left( 1 - 3 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
C)  $\frac { ( 2 x ) \left( 1 + 3 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$ 
D)  $\frac { ( 2 x ) \left( 1 - 5 x ^ { 2 } \right) } { \left( x ^ { 2 } + 1 \right) ^ { 5 } }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$$

Accepted Answer

A)  $\frac { 16 } { x }$ 
B)  $\frac { x } { 16 }$ 
C)  16 
D)  1 
A)  $\frac { 16 } { x }$ 
B)  $\frac { x } { 16 }$ 
C)  16 
D)  1

Evaluate the expression. - $\left( \frac { 1 } { 64 } \right) ^ { 7 / 3 }$

Factor by any method. - $125 a ^ { 3 } - 64 b ^ { 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 18 } } { x ^ { 4 } }$

Find the product or quotient. - $\frac { k ^ { 2 } + 6 k + 9 } { k ^ { 2 } + 11 k + 24 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 11 k + 24 }$

Write in radical form. Assume all variables represent positive real numbers. - $( - 6 x ) ^ { 1 / 5 }$

Tell whether the statement is true or false. - $5 \in \{ 3,43,5,6 \}$

Evaluate the expression. - $- \left| \frac { 8 } { 5 } \right|$

Determine which property of absolute value justifies the statement. - $| x | \geq 0$

Write in exponential form. Assume all variables are positive real numbers. - $\sqrt [ 3 ] { \mathrm { x } ^ { 5 } }$

Factor by any method. - $b ^ { 6 } - 64 a ^ { 6 }$

Find the product. - $( - 8 a - 9 b ) ( 9 a + 8 b )$

Solve the problem. -Find all values of $b$ that will make the polynomial a perfect square trinomial. $25 x ^ { 2 } + 40 x + b$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 4 } y ^ { 8 } } { x ^ { - 2 } y ^ { 5 } }$

Find the product. - $( n + 11 ) ^ { 2 }$

Factor, using the given factor. Assume all variables represent positive real numbers. - $8 m ^ { 3 / 4 } - 3 m - 1 / 2 ; \quad m ^ { - 1 / 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 5 ) ^ { - 2 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { \left( x ^ { 2 } + 1 \right) ^ { 4 } ( 2 x ) - x ^ { 2 } ( 4 ) \left( x ^ { 2 } + 1 \right) ^ { 3 } ( 2 x ) } { \left( x ^ { 2 } + 1 \right) ^ { 8 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$

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

Evaluate the expression. - (164)7/3\left( \frac { 1 } { 64 } \right) ^ { 7 / 3 }(641​)7/3

Factor by any method. - 125a3−64b3125 a ^ { 3 } - 64 b ^ { 3 }125a3−64b3

Simplify the expression. Assume all variables represent positive real numbers. - 2703103\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }310​3270​​

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x18x4\frac { x ^ { 18 } } { x ^ { 4 } }x4x18​

Find the product or quotient. - k2+6k+9k2+11k+24⋅k2+8kk2+11k+24\frac { k ^ { 2 } + 6 k + 9 } { k ^ { 2 } + 11 k + 24 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 11 k + 24 }k2+11k+24k2+6k+9​⋅k2+11k+24k2+8k​

Write in radical form. Assume all variables represent positive real numbers. - (−6x)1/5( - 6 x ) ^ { 1 / 5 }(−6x)1/5

Tell whether the statement is true or false. - 5∈{3,43,5,6}5 \in \{ 3,43,5,6 \}5∈{3,43,5,6}

Evaluate the expression. - −∣85∣- \left| \frac { 8 } { 5 } \right|−​58​​

Determine which property of absolute value justifies the statement. - ∣x∣≥0| x | \geq 0∣x∣≥0

Write in exponential form. Assume all variables are positive real numbers. - x53\sqrt [ 3 ] { \mathrm { x } ^ { 5 } }3x5​

Factor by any method. - b6−64a6b ^ { 6 } - 64 a ^ { 6 }b6−64a6

Find the product. - (−8a−9b)(9a+8b)( - 8 a - 9 b ) ( 9 a + 8 b )(−8a−9b)(9a+8b)

Solve the problem. -Find all values of bbb that will make the polynomial a perfect square trinomial. 25x2+40x+b25 x ^ { 2 } + 40 x + b25x2+40x+b

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x−4y8x−2y5\frac { x ^ { - 4 } y ^ { 8 } } { x ^ { - 2 } y ^ { 5 } }x−2y5x−4y8​

Find the product. - (n+11)2( n + 11 ) ^ { 2 }(n+11)2

Factor, using the given factor. Assume all variables represent positive real numbers. - 8m3/4−3m−1/2;m−1/28 m ^ { 3 / 4 } - 3 m - 1 / 2 ; \quad m ^ { - 1 / 2 }8m3/4−3m−1/2;m−1/2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−5)−2( - 5 ) ^ { - 2 }(−5)−2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 4+2xx4+18\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }4x​+81​4+x2​​