Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 5 ] { \frac { t ^ { 2 } } { 7776 } }$

Accepted Answer

A)  $\frac { \sqrt [ 5 ] { t } } { 6 }$ 
B)  $\frac { t } { 6 }$ 
C)  $\frac { \sqrt [ 5 ] { t ^ { 2 } } } { 6 }$ 
D)  $\sqrt { \frac { 5 t ^ { 2 } } { 7776 } }$ 
A)  $\frac { \sqrt [ 5 ] { t } } { 6 }$ 
B)  $\frac { t } { 6 }$ 
C)  $\frac { \sqrt [ 5 ] { t ^ { 2 } } } { 6 }$ 
D)  $\sqrt { \frac { 5 t ^ { 2 } } { 7776 } }$

Question 2

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

Accepted Answer

A)  $\frac { 2 x ^ { 16 } y ^ { 16 } } { z ^ { 8 } }$ 
B)  $\frac { 16 x ^ { 8 } y ^ { 8 } } { z ^ { 8 } }$ 
C)  $\frac { 16 x ^ { 16 } y ^ { 16 } } { z ^ { 16 } }$ 
D)  $\frac { 2 x ^ { 16 } y ^ { 16 } } { z ^ { 16 } }$ 
A)  $\frac { 2 x ^ { 16 } y ^ { 16 } } { z ^ { 8 } }$ 
B)  $\frac { 16 x ^ { 8 } y ^ { 8 } } { z ^ { 8 } }$ 
C)  $\frac { 16 x ^ { 16 } y ^ { 16 } } { z ^ { 16 } }$ 
D)  $\frac { 2 x ^ { 16 } y ^ { 16 } } { z ^ { 16 } }$

Question 3

Evaluate the expression.
-$( - 27 ) ^ { 2 / 3 }$

Accepted Answer

A)  not a real number 
B)  $- 9$ 
C)  9 
D)  $- 3$ 
A)  not a real number 
B)  $- 9$ 
C)  9 
D)  $- 3$

Question 4

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

Accepted Answer

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

Question 5

Simplify the expression. Assume all variables represent positive real numbers.
-$2 \sqrt { 10 } + 14 \sqrt { 10 }$

Accepted Answer

A)  $13 \sqrt { 10 }$ 
B)  $- 17 \sqrt { 10 }$ 
C)  $16 \sqrt { 10 }$ 
D)  $- 12 \sqrt { 10 }$ 
A)  $13 \sqrt { 10 }$ 
B)  $- 17 \sqrt { 10 }$ 
C)  $16 \sqrt { 10 }$ 
D)  $- 12 \sqrt { 10 }$

Question 6

Evaluate the expression.
-$3 ^ { 6 }$

Accepted Answer

A)  729 
B)  324 
C)  72.9 
D)  18 
A)  729 
B)  324 
C)  72.9 
D)  18

Question 7

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

Accepted Answer

A)  $x$ and $y$ must be positive. 
B)  $x$ and $y$ must be negative. 
C)  $x$ and $y$ have the same sign. 
D)  $x$ and $y$ have different signs. 
A)  $x$ and $y$ must be positive. 
B)  $x$ and $y$ must be negative. 
C)  $x$ and $y$ have the same sign. 
D)  $x$ and $y$ have different signs.

Question 8

Identify the set as finite or infinite.
-$\{ x \mid x \text { is a person alive now } \}$

Accepted Answer

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

Question 9

Factor out the greatest common factor. Simplify the factors, if possible.
-$10 x ^ { 2 } + 25 x + 6 x + 15$

Accepted Answer

A)  $( 10 x + 3 ) ( x + 5 )$ 
B)  $( 10 x - 3 ) ( x - 5 )$ 
C)  $( 5 x + 3 ) ( 2 x + 5 )$ 
D)  $( 5 x - 3 ) ( 2 x - 5 )$ 
A)  $( 10 x + 3 ) ( x + 5 )$ 
B)  $( 10 x - 3 ) ( x - 5 )$ 
C)  $( 5 x + 3 ) ( 2 x + 5 )$ 
D)  $( 5 x - 3 ) ( 2 x - 5 )$

Question 10

Factor the trinomial, if possible.
-$$- 2 x ^ { 3 } + 2 x ^ { 2 } + 40 x$$

Accepted Answer

A)  $- 2 x ( x + 5 ) ( x - 4 )$ 
B)  $- 2 x ( x - 5 ) ( x + 4 )$ 
C)  $- 2 x ^ { 2 } ( x - 5 ) ( x - 4 )$ 
D)  $2 x ( x + 5 ) ( x + 4 )$ 
A)  $- 2 x ( x + 5 ) ( x - 4 )$ 
B)  $- 2 x ( x - 5 ) ( x + 4 )$ 
C)  $- 2 x ^ { 2 } ( x - 5 ) ( x - 4 )$ 
D)  $2 x ( x + 5 ) ( x + 4 )$

Question 11

Find the sum or difference.
-$$( - 2 x - 9 ) ^ { 2 }$$

Accepted Answer

A)  $4 x ^ { 2 } + 81$ 
B)  $- 2 x ^ { 2 } + 81$ 
C)  $- 2 x ^ { 2 } + 36 x + 81$ 
D)  $4 x ^ { 2 } + 36 x + 81$ 
A)  $4 x ^ { 2 } + 81$ 
B)  $- 2 x ^ { 2 } + 81$ 
C)  $- 2 x ^ { 2 } + 36 x + 81$ 
D)  $4 x ^ { 2 } + 36 x + 81$

Question 12

Determine the degree of the polynomial.
-$- 2 x ^ { 2 } + 5 x ^ { 3 } + 6 x ^ { 4 } + 1$

Accepted Answer

A)  10 
B)  2 
C)  4 
D)  9 
A)  10 
B)  2 
C)  4 
D)  9

Question 13

Solve the problem. Round to two decimal places unless otherwise indicated.
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 262,500 } { x + 525 }$. What is the cost per ton for $x = 400$ ?

Accepted Answer

A)  $113,513.51 
B)  $131.25 
C)  $283.78 
D)  $200,000.00 
A)  $113,513.51 
B)  $131.25 
C)  $283.78 
D)  $200,000.00

Question 14

Use the distributive property to rewrite a sum as a product or the product as a sum.
-$$- ( - 3 - 9 b )$$

Accepted Answer

A)  $3 + 9 b$ 
B)  $- 3 + 9 b$ 
C)  $- 3 = 9 b$ 
D)  $3 - 9 b$ 
A)  $3 + 9 b$ 
B)  $- 3 + 9 b$ 
C)  $- 3 = 9 b$ 
D)  $3 - 9 b$

Question 15

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$- 8^0$

Accepted Answer

A)  $- 8$ 
B)  $- 1$ 
C)  0 
D)  1 
A)  $- 8$ 
B)  $- 1$ 
C)  0 
D)  1

Question 16

Factor by any method.
-$$( p + q ) ^ { 2 } - 2 ( p + q ) + 1$$

Accepted Answer

A)  prime 
B)  $( p + q - 1 ) ( p + q )$ 
C)  $( p + q - 1 ) ^ { 2 }$ 
D)  $( p + q - 1 ) ( p + q + 1 )$ 
A)  prime 
B)  $( p + q - 1 ) ( p + q )$ 
C)  $( p + q - 1 ) ^ { 2 }$ 
D)  $( p + q - 1 ) ( p + q + 1 )$

Question 17

Factor the trinomial, if possible.
-$108 m ^ { 2 } + 252 m n + 147 n ^ { 2 }$

Accepted Answer

A)  $3 ( 6 m + 7 n ) ^ { 2 }$ 
B)  $( 18 m - 3 n ) ^ { 2 }$ 
C)  $3 ( 6 m - 7 n ) ^ { 2 }$ 
D)  $( 18 m + 21 n ) ^ { 2 }$ 
A)  $3 ( 6 m + 7 n ) ^ { 2 }$ 
B)  $( 18 m - 3 n ) ^ { 2 }$ 
C)  $3 ( 6 m - 7 n ) ^ { 2 }$ 
D)  $( 18 m + 21 n ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 5 ] { \frac { t ^ { 2 } } { 7776 } }$

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

Evaluate the expression. - $( - 27 ) ^ { 2 / 3 }$

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

Simplify the expression. Assume all variables represent positive real numbers. - $2 \sqrt { 10 } + 14 \sqrt { 10 }$

Evaluate the expression. - $3 ^ { 6 }$

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

Identify the set as finite or infinite. - $\{ x \mid x \text { is a person alive now } \}$

Factor out the greatest common factor. Simplify the factors, if possible. - $10 x ^ { 2 } + 25 x + 6 x + 15$

Factor the trinomial, if possible. - $- 2 x ^ { 3 } + 2 x ^ { 2 } + 40 x$

Find the sum or difference. - $( - 2 x - 9 ) ^ { 2 }$

Determine the degree of the polynomial. - $- 2 x ^ { 2 } + 5 x ^ { 3 } + 6 x ^ { 4 } + 1$

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 262,500 } { x + 525 }$ . What is the cost per ton for $x = 400$ ?

Use the distributive property to rewrite a sum as a product or the product as a sum. - $- ( - 3 - 9 b )$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 8^0$

Factor by any method. - $( p + q ) ^ { 2 } - 2 ( p + q ) + 1$

Factor the trinomial, if possible. - $108 m ^ { 2 } + 252 m n + 147 n ^ { 2 }$

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Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - t277765\sqrt [ 5 ] { \frac { t ^ { 2 } } { 7776 } }57776t2​​

Simplify the expression. Assume all variables represent nonzero real numbers. - (2x4y4z4)4\left( \frac { 2 x ^ { 4 } y ^ { 4 } } { z ^ { 4 } } \right) ^ { 4 }(z42x4y4​)4

Evaluate the expression. - (−27)2/3( - 27 ) ^ { 2 / 3 }(−27)2/3

Factor the trinomial, if possible. - x2−x−45x ^ { 2 } - x - 45x2−x−45

Simplify the expression. Assume all variables represent positive real numbers. - 210+14102 \sqrt { 10 } + 14 \sqrt { 10 }210​+1410​

Evaluate the expression. - 363 ^ { 6 }36

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - −xy>0- \frac { x } { y } > 0−yx​>0

Identify the set as finite or infinite. - {x∣x is a person alive now }\{ x \mid x \text { is a person alive now } \}{x∣x is a person alive now }

Factor out the greatest common factor. Simplify the factors, if possible. - 10x2+25x+6x+1510 x ^ { 2 } + 25 x + 6 x + 1510x2+25x+6x+15

Factor the trinomial, if possible. - −2x3+2x2+40x- 2 x ^ { 3 } + 2 x ^ { 2 } + 40 x−2x3+2x2+40x

Find the sum or difference. - (−2x−9)2( - 2 x - 9 ) ^ { 2 }(−2x−9)2

Determine the degree of the polynomial. - −2x2+5x3+6x4+1- 2 x ^ { 2 } + 5 x ^ { 3 } + 6 x ^ { 4 } + 1−2x2+5x3+6x4+1

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose the cost per ton, yyy , to build an oil platform of xxx thousand tons is approximated by y=262,500x+525y = \frac { 262,500 } { x + 525 }y=x+525262,500​ . What is the cost per ton for x=400x = 400x=400 ?

Use the distributive property to rewrite a sum as a product or the product as a sum. - −(−3−9b)- ( - 3 - 9 b )−(−3−9b)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −80- 8^0−80

Factor by any method. - (p+q)2−2(p+q)+1( p + q ) ^ { 2 } - 2 ( p + q ) + 1(p+q)2−2(p+q)+1

Factor the trinomial, if possible. - 108m2+252mn+147n2108 m ^ { 2 } + 252 m n + 147 n ^ { 2 }108m2+252mn+147n2