Question 1

Factor, using the given factor. Assume all variables represent positive real numbers.
-$x ^ { 4 / 7 } + 3 x ^ { 2 / 7 } ; \quad x ^ { 2 / 7 }$

Accepted Answer

A)  $x ^ { 2 / 7 } \left( x ^ { 2 / 7 } + 3 \right)$ 
B)  $x ^ { 1 / 7 } \left( x ^ { 2 / 7 } + 3 \right)$ 
C)  $x ^ { 2 / 7 } \left( x ^ { - 2 / 7 } + 3 \right)$ 
D)  $x ^ { 1 / 7 } \left( x ^ { 4 / 7 } + 3 \right)$ 
A)  $x ^ { 2 / 7 } \left( x ^ { 2 / 7 } + 3 \right)$ 
B)  $x ^ { 1 / 7 } \left( x ^ { 2 / 7 } + 3 \right)$ 
C)  $x ^ { 2 / 7 } \left( x ^ { - 2 / 7 } + 3 \right)$ 
D)  $x ^ { 1 / 7 } \left( x ^ { 4 / 7 } + 3 \right)$

Question 2

Find the product. Assume variables represent positive real numbers.
-$- 3 k ^ { 1 / 8 } \left( 8 k ^ { 3 / 8 } - 6 k ^ { 3 / 4 } \right)$

Accepted Answer

A)  $- 24 \mathrm { k } ^ { 1 / 2 } + 18 \mathrm { k } ^ { 7 / 8 }$ 
B)  $- 24 \mathrm { k } ^ { 1 / 2 } - 18 \mathrm { k } ^ { 7 / 8 }$ 
C)  $- 24 \mathrm { k } ^ { 3 / 64 } + 18 \mathrm { k } ^ { 3 / 32 }$ 
D)  $- 24 k ^ { - 1 / 4 } - 18 k ^ { - 5 / 8 }$ 
A)  $- 24 \mathrm { k } ^ { 1 / 2 } + 18 \mathrm { k } ^ { 7 / 8 }$ 
B)  $- 24 \mathrm { k } ^ { 1 / 2 } - 18 \mathrm { k } ^ { 7 / 8 }$ 
C)  $- 24 \mathrm { k } ^ { 3 / 64 } + 18 \mathrm { k } ^ { 3 / 32 }$ 
D)  $- 24 k ^ { - 1 / 4 } - 18 k ^ { - 5 / 8 }$

Question 3

Evaluate the expression.
-(6 + (-5))[8 + (2 + 8)]

Accepted Answer

A)  98 
B)  18 
C)  15 
D)  19 
A)  98 
B)  18 
C)  15 
D)  19

Question 4

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { a ^ { 5 } } { b ^ { 10 } }$ 
B)  $\frac { a ^ { 10 } } { b ^ { 8 } }$ 
C)  $\frac { a ^ { 8 } } { b ^ { 5 } }$ 
D)  $\frac { a ^ { 8 } } { b ^ { 10 } }$ 
A)  $\frac { a ^ { 5 } } { b ^ { 10 } }$ 
B)  $\frac { a ^ { 10 } } { b ^ { 8 } }$ 
C)  $\frac { a ^ { 8 } } { b ^ { 5 } }$ 
D)  $\frac { a ^ { 8 } } { b ^ { 10 } }$

Question 5

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

Accepted Answer

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

Question 6

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 4 n ^ { 2 } \right) \cdot \left( 6 n ^ { 7 } \right)$

Accepted Answer

A)  $24 n ^ { 9 }$ 
B)  $24 n ^{14}$ 
C)  $10 \mathrm { n } ^ { 14 }$ 
D)  $10 n ^ { 9 }$ 
A)  $24 n ^ { 9 }$ 
B)  $24 n ^{14}$ 
C)  $10 \mathrm { n } ^ { 14 }$ 
D)  $10 n ^ { 9 }$

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 63 x ^ { 2 } y }$

Accepted Answer

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

Question 8

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-10 $\{ 7,8,9,10 \}$

Accepted Answer

A)  $\mathrm { }  \notin$ 
B)  $\epsilon$ 
A)  $\mathrm { }  \notin$ 
B)  $\epsilon$

Question 9

Factor the trinomial, if possible.
-$\mathrm { u } ^ { 2 } - 5 \mathrm { uv } - 36 \mathrm { v } ^ { 2 }$

Accepted Answer

A)  $( u - v ) ( u + 9 v )$ 
B)  $( u + 4 v ) ( u - 9 v )$ 
C)  $( u - 4 v ) ( u + v )$ 
D)  $( u - 4 v ) ( u + 9 v )$ 
A)  $( u - v ) ( u + 9 v )$ 
B)  $( u + 4 v ) ( u - 9 v )$ 
C)  $( u - 4 v ) ( u + v )$ 
D)  $( u - 4 v ) ( u + 9 v )$

Question 10

Simplify the expression.
-$\sqrt { 49 x ^ { 2 } }$

Accepted Answer

A)  $- 7 x$ 
B)  $49 x$ 
C)  $7 x ^ { 2 }$ 
D)  $7 | x |$ 
A)  $- 7 x$ 
B)  $49 x$ 
C)  $7 x ^ { 2 }$ 
D)  $7 | x |$

Question 11

Evaluate the expression for x = -2, y = 3, and a = -4.
--2a - 6y + 3x

Accepted Answer

A)  -16 
B)  4 
C)  29 
D)  37 
A)  -16 
B)  4 
C)  29 
D)  37

Question 12

Use set notation, and list all the elements of the set.
-The natural numbers between 3 and 9 .

Accepted Answer

A)  $\{ 3,4,5,6,7,8,9 \}$ 
B)  $\{ 4,5,6,7,8 \}$ 
C)  $\{ 0,1,2,3 \}$ 
D)  $\{ 3,9 \}$ 
A)  $\{ 3,4,5,6,7,8,9 \}$ 
B)  $\{ 4,5,6,7,8 \}$ 
C)  $\{ 0,1,2,3 \}$ 
D)  $\{ 3,9 \}$

Question 13

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 9,10,11,12,13,14 \} , \mathrm { B } = \{ 11,13,15 \} , \mathrm { C } = \{ 9,10,12,14 \} , \mathrm { D } = \{ 9,14 \}$, and $\mathrm { U } = \{ 9,10,11,12,13,14,15 \}$
$\mathrm { A } \subseteq \mathrm { U }$

Accepted Answer

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

Question 14

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| 3 - 9 | = | 9 | - | 3 |$$

Accepted Answer

A)  True 
B)  False; $| 3 - 9 | = | 3 | - | 9 |$ 
A)  True 
B)  False; $| 3 - 9 | = | 3 | - | 9 |$

Question 15

Find the product.
-$$[ ( 5 x + 1 ) + 3 y ] ^ { 2 }$$

Accepted Answer

A)  $25 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$ 
B)  $25 x ^ { 2 } + 10 x + 1 + 30 x y + 6 y + 9 y ^ { 2 }$ 
C)  $25 x ^ { 2 } + 5 x + 1 + 15 x y + 3 y + 9 y ^ { 2 }$ 
D)  $25 x ^ { 2 } + 10 x + 30 x y + 6 y + 9 y ^ { 2 }$ 
A)  $25 x ^ { 2 } + 30 x y + 9 y ^ { 2 }$ 
B)  $25 x ^ { 2 } + 10 x + 1 + 30 x y + 6 y + 9 y ^ { 2 }$ 
C)  $25 x ^ { 2 } + 5 x + 1 + 15 x y + 3 y + 9 y ^ { 2 }$ 
D)  $25 x ^ { 2 } + 10 x + 30 x y + 6 y + 9 y ^ { 2 }$

Question 16

Evaluate the expression.
-Let $\mathrm { x } = - 24 , \mathrm { y } = 1$. Evaluate $| 20 \mathrm { x } |$.

Accepted Answer

A)  $- 480$ 
B)  24 
C)  $- 24$ 
D)  480 
A)  $- 480$ 
B)  24 
C)  $- 24$ 
D)  480

Question 17

Evaluate the expression.
-$- 3^6$

Accepted Answer

A)  $- 18$ 
B)  $- 729$ 
C)  18 
D)  729 
A)  $- 18$ 
B)  $- 729$ 
C)  18 
D)  729

Question 18

Factor the trinomial, if possible.
-$40 m ^ { 2 } + 41 m n + 10 n ^ { 2 }$

Accepted Answer

A)  $( 8 m + 5 n ) ( 5 m + 2 n )$ 
B)  $( 8 m + 2 n ) ( 5 m + 5 n )$ 
C)  $( 8 m - 5 n ) ( 5 m - 2 n )$ 
D)  $\left( 8 m + 5 n ^ { 2 } \right) ( 5 m + 2 )$ 
A)  $( 8 m + 5 n ) ( 5 m + 2 n )$ 
B)  $( 8 m + 2 n ) ( 5 m + 5 n )$ 
C)  $( 8 m - 5 n ) ( 5 m - 2 n )$ 
D)  $\left( 8 m + 5 n ^ { 2 } \right) ( 5 m + 2 )$

Question 19

Find the product.
-$$( x + 12 ) ( 3 x - 10 )$$

Accepted Answer

A)  $3 x ^ { 2 } + 26 x - 120$ 
B)  $3 x ^ { 2 } + 26 x + 26$ 
C)  $3 x ^ { 2 } + 24 x - 120$ 
D)  $3 x ^ { 2 } - 120 x + 26$ 
A)  $3 x ^ { 2 } + 26 x - 120$ 
B)  $3 x ^ { 2 } + 26 x + 26$ 
C)  $3 x ^ { 2 } + 24 x - 120$ 
D)  $3 x ^ { 2 } - 120 x + 26$

Question 20

Solve the problem.
-Find the magnitude of the difference between a windchill factor of -43 and a windchill factor of -13.

Accepted Answer

A)  -30 
B)  -56 
C)  56 
D)  30 
A)  -30 
B)  -56 
C)  56 
D)  30

Factor, using the given factor. Assume all variables represent positive real numbers. - $x ^ { 4 / 7 } + 3 x ^ { 2 / 7 } ; \quad x ^ { 2 / 7 }$

Find the product. Assume variables represent positive real numbers. - $- 3 k ^ { 1 / 8 } \left( 8 k ^ { 3 / 8 } - 6 k ^ { 3 / 4 } \right)$

Evaluate the expression. -(6 + (-5))[8 + (2 + 8)]

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 2 }$

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

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 4 n ^ { 2 } \right) \cdot \left( 6 n ^ { 7 } \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 63 x ^ { 2 } y }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -10 $\{ 7,8,9,10 \}$

Factor the trinomial, if possible. - $\mathrm { u } ^ { 2 } - 5 \mathrm { uv } - 36 \mathrm { v } ^ { 2 }$

Simplify the expression. - $\sqrt { 49 x ^ { 2 } }$

Evaluate the expression for x = -2, y = 3, and a = -4. --2a - 6y + 3x

Use set notation, and list all the elements of the set. -The natural numbers between 3 and 9 .

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 9,10,11,12,13,14 \} , \mathrm { B } = \{ 11,13,15 \} , \mathrm { C } = \{ 9,10,12,14 \} , \mathrm { D } = \{ 9,14 \}$ , and $\mathrm { U } = \{ 9,10,11,12,13,14,15 \}$ $\mathrm { A } \subseteq \mathrm { U }$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| 3 - 9 | = | 9 | - | 3 |$

Find the product. - $[ ( 5 x + 1 ) + 3 y ] ^ { 2 }$

Evaluate the expression. -Let $\mathrm { x } = - 24 , \mathrm { y } = 1$ . Evaluate $| 20 \mathrm { x } |$ .

Evaluate the expression. - $- 3^6$

Factor the trinomial, if possible. - $40 m ^ { 2 } + 41 m n + 10 n ^ { 2 }$

Find the product. - $( x + 12 ) ( 3 x - 10 )$

Solve the problem. -Find the magnitude of the difference between a windchill factor of -43 and a windchill factor of -13.

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Exam 12: Review of Basic Concepts

Factor, using the given factor. Assume all variables represent positive real numbers. - x4/7+3x2/7;x2/7x ^ { 4 / 7 } + 3 x ^ { 2 / 7 } ; \quad x ^ { 2 / 7 }x4/7+3x2/7;x2/7

Find the product. Assume variables represent positive real numbers. - −3k1/8(8k3/8−6k3/4)- 3 k ^ { 1 / 8 } \left( 8 k ^ { 3 / 8 } - 6 k ^ { 3 / 4 } \right)−3k1/8(8k3/8−6k3/4)