Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 48 x ^ { 2 } y } { 49 } }$$

Accepted Answer

A)  $\frac { 4 \sqrt { 3 x ^ { 2 } y } } { 7 }$ 
B)  $\frac { 4 x \sqrt { 3 y } } { 7 }$ 
C)  $x \sqrt { \frac { 48 y } { 7 } }$ 
D)  $16 x \sqrt { 3 y }$ 
A)  $\frac { 4 \sqrt { 3 x ^ { 2 } y } } { 7 }$ 
B)  $\frac { 4 x \sqrt { 3 y } } { 7 }$ 
C)  $x \sqrt { \frac { 48 y } { 7 } }$ 
D)  $16 x \sqrt { 3 y }$

Question 2

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( x ^ { 4 } \right) ^ { 3 }$

Accepted Answer

A)  $x ^ { 12 }$ 
B)  $3 x ^ { 4 }$ 
C)  $12 x$ 
D)  $x ^ { 7 }$ 
A)  $x ^ { 12 }$ 
B)  $3 x ^ { 4 }$ 
C)  $12 x$ 
D)  $x ^ { 7 }$

Question 3

Factor out the greatest common factor. Simplify the factors, if possible.
-$108 x ^ { 7 } y ^ { 8 } - 24 x ^ { 2 } y ^ { 6 } + 96 x ^ { 5 } y ^ { 4 }$

Accepted Answer

A)  $x ^ { 2 } y ^ { 4 } \left( 108 x ^ { 5 } y ^ { 4 } - 24 y ^ { 2 } + 96 x ^ { 3 } \right)$ 
B)  $12 \left( 9 x ^ { 7 } y ^ { 8 } - 2 x ^ { 2 } y ^ { 6 } + 8 x ^ { 5 } y ^ { 4 } \right)$ 
C)  $12 x ^ { 2 } y ^ { 4 } \left( 9 x ^ { 5 } y ^ { 4 } - 2 y ^ { 2 } + 8 x ^ { 3 } \right)$ 
D)  $12 x ^ { 2 } \left( 9 x ^ { 5 } y ^ { 8 } - 2 y ^ { 6 } + 8 x ^ { 3 } y ^ { 4 } \right)$ 
A)  $x ^ { 2 } y ^ { 4 } \left( 108 x ^ { 5 } y ^ { 4 } - 24 y ^ { 2 } + 96 x ^ { 3 } \right)$ 
B)  $12 \left( 9 x ^ { 7 } y ^ { 8 } - 2 x ^ { 2 } y ^ { 6 } + 8 x ^ { 5 } y ^ { 4 } \right)$ 
C)  $12 x ^ { 2 } y ^ { 4 } \left( 9 x ^ { 5 } y ^ { 4 } - 2 y ^ { 2 } + 8 x ^ { 3 } \right)$ 
D)  $12 x ^ { 2 } \left( 9 x ^ { 5 } y ^ { 8 } - 2 y ^ { 6 } + 8 x ^ { 3 } y ^ { 4 } \right)$

Question 4

Identify the set as finite or infinite.
-{9, 12, 15, . . ., 24}

Accepted Answer

A)  infinite 
B)  finite 
A)  infinite 
B)  finite

Question 5

Solve the problem.
-$$( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)$$

Accepted Answer

A)  $x ^ { 4 } - 100 x ^ { 2 } + 625$ 
B)  $x ^ { 4 } - 625$ 
C)  $x ^ { 4 } - 25$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } - 25$ 
A)  $x ^ { 4 } - 100 x ^ { 2 } + 625$ 
B)  $x ^ { 4 } - 625$ 
C)  $x ^ { 4 } - 25$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } - 25$

Question 6

Evaluate the expression.
-$- 5 ( - 4 ) ^ { 3 }$

Accepted Answer

A)  -320 
B)  320 
C)  -8,000 
D)  8,000 
A)  -320 
B)  320 
C)  -8,000 
D)  8,000

Question 7

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-(2 ·6) ·8 = 2 · (6 ·8)

Accepted Answer

A)  Commutative 
B)  Associative 
C)  Identity 
D)  Distributive 
A)  Commutative 
B)  Associative 
C)  Identity 
D)  Distributive

Question 8

Identify the expression as a polynomial or not a polynomial.
-15x - 12

Accepted Answer

A)  Polynomial 
B)  Not a polynomial 
A)  Polynomial 
B)  Not a polynomial

Question 9

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 11 , \sqrt { 7 } , - 18,0 , \frac { 0 } { 2 } , \sqrt { 16 } \right\}$$
Integers

Accepted Answer

A)  $11 , - 18,0$ 
B)  11,0 
C)  $11,0 , \sqrt { 16 }$ 
D)  $11 , - 18,0 , \frac { 0 } { 2 } , \sqrt { 16 }$ 
A)  $11 , - 18,0$ 
B)  11,0 
C)  $11,0 , \sqrt { 16 }$ 
D)  $11 , - 18,0 , \frac { 0 } { 2 } , \sqrt { 16 }$

Question 10

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { - 4 } { \sqrt [ 3 ] { 3 } } + \frac { 32 } { \sqrt [ 3 ] { 24 } } - \frac { 1 } { \sqrt [ 3 ] { 81 } }$$

Accepted Answer

A)  $\frac { 73 } { 18 } \sqrt [ 3 ] { 9 }$ 
B)  $\frac { 17 } { 3 } \sqrt [ 3 ] { 3 }$ 
C)  $\frac { 35 } { 9 } \sqrt [ 3 ] { 9 }$ 
D)  $\frac { 35 } { 3 } \sqrt [ 3 ] { 3 }$ 
A)  $\frac { 73 } { 18 } \sqrt [ 3 ] { 9 }$ 
B)  $\frac { 17 } { 3 } \sqrt [ 3 ] { 3 }$ 
C)  $\frac { 35 } { 9 } \sqrt [ 3 ] { 9 }$ 
D)  $\frac { 35 } { 3 } \sqrt [ 3 ] { 3 }$

Question 11

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { 16 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 64 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 256 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$$

Accepted Answer

A)  $\frac { 1 - 4 x ^ { 3 } + 12 x } { 64 }$ 
B)  $\frac { 1 - 4 x ^ { 3 } - 12 x } { 64 }$ 
C)  $\frac { 1 + 4 x ^ { 3 } - 12 x } { 16 }$ 
D)  $\frac { 1 + 4 x ^ { 3 } + 12 x } { 16 }$ 
A)  $\frac { 1 - 4 x ^ { 3 } + 12 x } { 64 }$ 
B)  $\frac { 1 - 4 x ^ { 3 } - 12 x } { 64 }$ 
C)  $\frac { 1 + 4 x ^ { 3 } - 12 x } { 16 }$ 
D)  $\frac { 1 + 4 x ^ { 3 } + 12 x } { 16 }$

Question 12

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( x ^ { 8 } y ^ { 9 } \right) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 4096 } y ^{6561}$ 
B)  $x ^ { 8 } y ^ { 36 }$ 
C)  $x ^ { 12 } y ^ { 13 }$ 
D)  $x ^ { 32 } y ^ { 36 }$ 
A)  $x ^ { 4096 } y ^{6561}$ 
B)  $x ^ { 8 } y ^ { 36 }$ 
C)  $x ^ { 12 } y ^ { 13 }$ 
D)  $x ^ { 32 } y ^ { 36 }$

Question 13

Answer the question.
-$$[ ( 5 x - y ) + 3 z ] [ ( 5 x - y ) - 3 z ]$$

Accepted Answer

A)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } - 9 z ^ { 2 }$ 
B)  $25 x ^ { 2 } + y ^ { 2 } - 9 z ^ { 2 }$ 
C)  $25 x ^ { 2 } + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
D)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
A)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } - 9 z ^ { 2 }$ 
B)  $25 x ^ { 2 } + y ^ { 2 } - 9 z ^ { 2 }$ 
C)  $25 x ^ { 2 } + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
D)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$

Question 14

Evaluate the expression.
-$$\left| - \frac { 10 } { 3 } \right|$$

Accepted Answer

A)  0 
B)  $\pm \frac { 10 } { 3 }$ 
C)  $\frac { 10 } { 3 }$ 
D)  $- \frac { 10 } { 3 }$ 
A)  0 
B)  $\pm \frac { 10 } { 3 }$ 
C)  $\frac { 10 } { 3 }$ 
D)  $- \frac { 10 } { 3 }$

Question 15

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { 4 x + 4 ( 3 + a ) ^ { 2 } } { y - 1 }$$

Accepted Answer

A)  18 
B)  $- 2$ 
C)  38 
D)  66 
A)  18 
B)  $- 2$ 
C)  38 
D)  66

Question 16

Identify the expression as a polynomial or not a polynomial.
-$5 x ^ { 2 } y ^ { 3 } + 4 x ^ { 3 } y + 5 x$

Accepted Answer

A)  Not a polynomial 
B)  Polynomial 
A)  Not a polynomial 
B)  Polynomial

Question 17

Factor, using the given factor. Assume all variables represent positive real numbers.
-$$x ^ { 6 / 8 } + 3 x ^ { 5 / 8 } ; \quad x ^ { 5 / 8 }$$

Accepted Answer

A)  $x 1 / 8 \left( x ^ { 6 / 8 } + 3 \right)$ 
B)  $x ^ { 5 / 8 } \left( x ^ { 1 / 8 } + 3 \right)$ 
C)  $x ^ { 1 / 8 } \left( x ^ { 1 / 8 } + 3 \right)$ 
D)  $x ^ { 5 / 8 } \left( x ^ { - 1 / 8 } + 3 \right)$ 
A)  $x 1 / 8 \left( x ^ { 6 / 8 } + 3 \right)$ 
B)  $x ^ { 5 / 8 } \left( x ^ { 1 / 8 } + 3 \right)$ 
C)  $x ^ { 1 / 8 } \left( x ^ { 1 / 8 } + 3 \right)$ 
D)  $x ^ { 5 / 8 } \left( x ^ { - 1 / 8 } + 3 \right)$

Question 18

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { 4 ^ { - 7 } } { 4 ^ { - 4 } }$$

Accepted Answer

A)  $\frac { 1 } { 4 ^ { 11 } }$ 
B)  $\frac { 1 } { 4 ^ { 3 } }$ 
C)  $4 ^ { 3 }$ 
D)  411 
A)  $\frac { 1 } { 4 ^ { 11 } }$ 
B)  $\frac { 1 } { 4 ^ { 3 } }$ 
C)  $4 ^ { 3 }$ 
D)  411

Question 19

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

Accepted Answer

A)  $x ^ { 1 / 15 }$ 
B)  $x ^ { 5 / 3 }$ 
C)  $x ^ { 3 / 5 }$ 
D)  $x ^ { 3 / 15 }$ 
A)  $x ^ { 1 / 15 }$ 
B)  $x ^ { 5 / 3 }$ 
C)  $x ^ { 3 / 5 }$ 
D)  $x ^ { 3 / 15 }$

Question 20

Factor the trinomial, if possible.
-$x ^ { 2 } - x - 45$

Accepted Answer

A)  $( x + 5 ) ( x - 9 )$ 
B)  prime 
C)  $( x - 5 ) ( x + 9 )$ 
D)  $( x - 45 ) ( x + 1 )$ 
A)  $( x + 5 ) ( x - 9 )$ 
B)  prime 
C)  $( x - 5 ) ( x + 9 )$ 
D)  $( x - 45 ) ( x + 1 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 48 x ^ { 2 } y } { 49 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( x ^ { 4 } \right) ^ { 3 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $108 x ^ { 7 } y ^ { 8 } - 24 x ^ { 2 } y ^ { 6 } + 96 x ^ { 5 } y ^ { 4 }$

Identify the set as finite or infinite. -{9, 12, 15, . . ., 24}

Solve the problem. - $( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)$

Evaluate the expression. - $- 5 ( - 4 ) ^ { 3 }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -(2 ·6) ·8 = 2 · (6 ·8)

Identify the expression as a polynomial or not a polynomial. -15x - 12

List all the elements of set B that belong to the indicated set. - $B = \left\{ 11 , \sqrt { 7 } , - 18,0 , \frac { 0 } { 2 } , \sqrt { 16 } \right\}$ Integers

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { - 4 } { \sqrt [ 3 ] { 3 } } + \frac { 32 } { \sqrt [ 3 ] { 24 } } - \frac { 1 } { \sqrt [ 3 ] { 81 } }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { 16 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 64 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 256 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( x ^ { 8 } y ^ { 9 } \right) ^ { 4 }$

Answer the question. - $[ ( 5 x - y ) + 3 z ] [ ( 5 x - y ) - 3 z ]$

Evaluate the expression. - $\left| - \frac { 10 } { 3 } \right|$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { 4 x + 4 ( 3 + a ) ^ { 2 } } { y - 1 }$

Identify the expression as a polynomial or not a polynomial. - $5 x ^ { 2 } y ^ { 3 } + 4 x ^ { 3 } y + 5 x$

Factor, using the given factor. Assume all variables represent positive real numbers. - $x ^ { 6 / 8 } + 3 x ^ { 5 / 8 } ; \quad x ^ { 5 / 8 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 4 ^ { - 7 } } { 4 ^ { - 4 } }$

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

Factor the trinomial, if possible. - $x ^ { 2 } - x - 45$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

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Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 48x2y49\sqrt { \frac { 48 x ^ { 2 } y } { 49 } }4948x2y​​

Simplify the expression. Assume all variables represent nonzero real numbers. - (x4)3\left( x ^ { 4 } \right) ^ { 3 }(x4)3

Factor out the greatest common factor. Simplify the factors, if possible. - 108x7y8−24x2y6+96x5y4108 x ^ { 7 } y ^ { 8 } - 24 x ^ { 2 } y ^ { 6 } + 96 x ^ { 5 } y ^ { 4 }108x7y8−24x2y6+96x5y4