Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 75 }$

Accepted Answer

A)  5 
B)  8 
C)  $25 \sqrt { 3 }$ 
D)  $5 \sqrt { 3 }$ 
A)  5 
B)  8 
C)  $25 \sqrt { 3 }$ 
D)  $5 \sqrt { 3 }$

Question 2

Find the product.
-$$( 4 x + 5 ) ^ { 3 }$$

Accepted Answer

A)  $16 x ^ { 2 } + 40 x + 25$ 
B)  $64 x ^ { 3 } + 240 x ^ { 2 } + 300 x + 125$ 
C)  $64 x ^ { 3 } + 240 x ^ { 2 } + 240 x + 125$ 
D)  $16 x ^ { 6 } + 20 x ^ { 3 } + 15,625$ 
A)  $16 x ^ { 2 } + 40 x + 25$ 
B)  $64 x ^ { 3 } + 240 x ^ { 2 } + 300 x + 125$ 
C)  $64 x ^ { 3 } + 240 x ^ { 2 } + 240 x + 125$ 
D)  $16 x ^ { 6 } + 20 x ^ { 3 } + 15,625$

Question 3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( - 2 ) ^ { 0 }$

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  $- 1$ 
A)  1 
B)  2 
C)  0 
D)  $- 1$

Question 4

Identify the expression as a polynomial or not a polynomial.
-$4 x ^ { 4 } + 6 x ^ { 3 } - 18$

Accepted Answer

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

Question 5

Factor out the greatest common factor. Simplify the factors, if possible.
-$$( x - 9 ) ( x + 7 ) + ( x - 9 ) ( x + 7 )$$

Accepted Answer

A)  $2 ( x - 9 ) ( 2 x + 14 )$ 
B)  $2 ( x - 9 ) ( x + 7 )$ 
C)  $( x - 9 ) ( 2 x + 14 )$ 
D)  $( x - 9 ) ( x + 14 )$ 
A)  $2 ( x - 9 ) ( 2 x + 14 )$ 
B)  $2 ( x - 9 ) ( x + 7 )$ 
C)  $( x - 9 ) ( 2 x + 14 )$ 
D)  $( x - 9 ) ( x + 14 )$

Question 6

Solve the problem.
-The formula $C = \frac { 5 } { 9 } ( F - 32 )$ expresses the relationship between Fahrenheit temperature, $F$, and Celsius temperature, C. Use the formula to convert $86 ^ { \circ } \mathrm { F }$ to its equivalent temperature on the Celsius scale.

Accepted Answer

A)  $66 ^ { \circ } \mathrm { C }$ 
B)  $97 ^ { \circ } \mathrm { C }$ 
C)  $30 ^ { \circ } \mathrm { C }$ 
D)  $6 ^ { \circ } \mathrm { C }$ 
A)  $66 ^ { \circ } \mathrm { C }$ 
B)  $97 ^ { \circ } \mathrm { C }$ 
C)  $30 ^ { \circ } \mathrm { C }$ 
D)  $6 ^ { \circ } \mathrm { C }$

Question 7

Use the distributive property to rewrite a sum as a product or the product as a sum.
--2a + 17a

Accepted Answer

A)  15a 
B)  -19a 
C)  19a 
D)  -15a 
A)  15a 
B)  -19a 
C)  19a 
D)  -15a

Question 8

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$$

Accepted Answer

A)  $\frac { 24 x - 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
B)  $\frac { 26 x + 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
C)  $\frac { 26 x - 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
D)  $\frac { 24 x + 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
A)  $\frac { 24 x - 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
B)  $\frac { 26 x + 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
C)  $\frac { 26 x - 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
D)  $\frac { 24 x + 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$

Question 9

Identify the expression as a polynomial or not a polynomial.
-5

Accepted Answer

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

Question 10

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 2 x } + \sqrt { 3 y } }$

Accepted Answer

A)  $\frac { x \sqrt { 2 } - \sqrt { 3 x y } - \sqrt { 2 x y } + y \sqrt { 3 } } { 2 x - 3 y }$ 
B)  $\frac { \sqrt { 2 x } - \sqrt { 5 x y } + \sqrt { 3 y } } { 2 x + 3 y }$ 
C)  $\frac { x \sqrt { 2 } - \sqrt { 3 x y } - \sqrt { 2 x y } + y \sqrt { 3 } } { 2 x + 3 y }$ 
D)  $\frac { \sqrt { 2 x } - \sqrt { 5 x y } + \sqrt { 3 y } } { 2 x - 3 y }$ 
A)  $\frac { x \sqrt { 2 } - \sqrt { 3 x y } - \sqrt { 2 x y } + y \sqrt { 3 } } { 2 x - 3 y }$ 
B)  $\frac { \sqrt { 2 x } - \sqrt { 5 x y } + \sqrt { 3 y } } { 2 x + 3 y }$ 
C)  $\frac { x \sqrt { 2 } - \sqrt { 3 x y } - \sqrt { 2 x y } + y \sqrt { 3 } } { 2 x + 3 y }$ 
D)  $\frac { \sqrt { 2 x } - \sqrt { 5 x y } + \sqrt { 3 y } } { 2 x - 3 y }$

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { \frac { 256 } { 81 } }$

Accepted Answer

A)  $\frac { 256 } { 81 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $\frac { 16 } { 9 }$ 
D)  $\frac { 64 } { 27 }$ 
A)  $\frac { 256 } { 81 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $\frac { 16 } { 9 }$ 
D)  $\frac { 64 } { 27 }$

Question 12

Solve the problem.
-A formula for calculating the distance, d, one can see from an airplane to the horizon on a clear day is $$\mathrm { d } = 1.22 \mathrm { x } ^ { 1 / 2 }$$ where x is the altitude of the plane in feet and d is given in miles. How far can
One see in a plane flying at 28,000 feet? Round your answer to the nearest tenth mile, if necessary.

Accepted Answer

A)  184.8 mi 
B)  204.1 mi 
C)  17,080 mi 
D)  1708 mi 
A)  184.8 mi 
B)  204.1 mi 
C)  17,080 mi 
D)  1708 mi

Question 13

Tell whether the statement is true or false.
-$\{ x \mid x$ is a natural number greater than $6 \} = \{ 6,7,8 , \ldots \}$

Accepted Answer

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

Question 14

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$4 ^ { - 2 }$

Accepted Answer

A)  $\frac { 1 } { 16 }$ 
B)  $- 16$ 
C)  $- 8$ 
D)  $- \frac { 1 } { 16 }$ 
A)  $\frac { 1 } { 16 }$ 
B)  $- 16$ 
C)  $- 8$ 
D)  $- \frac { 1 } { 16 }$

Question 15

Find the domain of the expression.
-$$\frac { 7 x - 8 } { ( 3 x - 2 ) ( x + 9 ) }$$

Accepted Answer

A)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 2 } , - 9 \right\} \right.$ 
B)  $\left\{ \left\{ x \mid x \neq \frac { 2 } { 3 } , - 9 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq - \frac { 2 } { 3 } , 9 \right\} \right.$ 
D)  all real numbers 
A)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 2 } , - 9 \right\} \right.$ 
B)  $\left\{ \left\{ x \mid x \neq \frac { 2 } { 3 } , - 9 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq - \frac { 2 } { 3 } , 9 \right\} \right.$ 
D)  all real numbers

Question 16

Divide.
-$$\frac { - 21 x ^ { 1 } - 30 x ^ { - 3 } } { 3 x ^ { - 7 } }$$

Accepted Answer

A)  $- 7 x ^ { 8 } - 30 x - 3$ 
B)  $- 7 x ^ { 8 } - 10 x ^ { 4 }$ 
C)  $- 21 x ^ { 1 } - 10 x ^ { 4 }$ 
D)  $- 17 x ^ { 5 }$ 
A)  $- 7 x ^ { 8 } - 30 x - 3$ 
B)  $- 7 x ^ { 8 } - 10 x ^ { 4 }$ 
C)  $- 21 x ^ { 1 } - 10 x ^ { 4 }$ 
D)  $- 17 x ^ { 5 }$

Question 17

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|$$

Accepted Answer

A)  True 
B)  False; $\left| ( - 5 ) ^ { 3 } \right| = 5 ^ { 3 }$ 
A)  True 
B)  False; $\left| ( - 5 ) ^ { 3 } \right| = 5 ^ { 3 }$

Question 18

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }$

Accepted Answer

A)  $\frac { \sqrt { 55 } + 2 \sqrt { 5 } } { 7 }$ 
B)  $\frac { 3 \sqrt { 55 } + 115 } { 22 }$ 
C)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 7 }$ 
D)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 13 }$ 
A)  $\frac { \sqrt { 55 } + 2 \sqrt { 5 } } { 7 }$ 
B)  $\frac { 3 \sqrt { 55 } + 115 } { 22 }$ 
C)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 7 }$ 
D)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 13 }$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 512 }$

Accepted Answer

A)  64 
B)  23 
C)  8 
D)  $\pm 8$ 
A)  64 
B)  23 
C)  8 
D)  $\pm 8$

Question 20

Solve the problem.
-Find the magnitude of the difference between a windchill factor of 88 and a windchill factor of -77.

Accepted Answer

A)  -165 
B)  165 
C)  11 
D)  -11 
A)  -165 
B)  165 
C)  11 
D)  -11

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 75 }$

Find the product. - $( 4 x + 5 ) ^ { 3 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 2 ) ^ { 0 }$

Identify the expression as a polynomial or not a polynomial. - $4 x ^ { 4 } + 6 x ^ { 3 } - 18$

Factor out the greatest common factor. Simplify the factors, if possible. - $( x - 9 ) ( x + 7 ) + ( x - 9 ) ( x + 7 )$

Solve the problem. -The formula $C = \frac { 5 } { 9 } ( F - 32 )$ expresses the relationship between Fahrenheit temperature, $F$ , and Celsius temperature, C. Use the formula to convert $86 ^ { \circ } \mathrm { F }$ to its equivalent temperature on the Celsius scale.

Use the distributive property to rewrite a sum as a product or the product as a sum. --2a + 17a

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$

Identify the expression as a polynomial or not a polynomial. -5

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 2 x } + \sqrt { 3 y } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 256 } { 81 } }$

Tell whether the statement is true or false. - $\{ x \mid x$ is a natural number greater than $6 \} = \{ 6,7,8 , \ldots \}$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $4 ^ { - 2 }$

Find the domain of the expression. - $\frac { 7 x - 8 } { ( 3 x - 2 ) ( x + 9 ) }$

Divide. - $\frac { - 21 x ^ { 1 } - 30 x ^ { - 3 } } { 3 x ^ { - 7 } }$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 512 }$

Solve the problem. -Find the magnitude of the difference between a windchill factor of 88 and a windchill factor of -77.

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Exam 12: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 75\sqrt { 75 }75​

Find the product. - (4x+5)3( 4 x + 5 ) ^ { 3 }(4x+5)3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−2)0( - 2 ) ^ { 0 }(−2)0

Identify the expression as a polynomial or not a polynomial. - 4x4+6x3−184 x ^ { 4 } + 6 x ^ { 3 } - 184x4+6x3−18

Factor out the greatest common factor. Simplify the factors, if possible. - (x−9)(x+7)+(x−9)(x+7)( x - 9 ) ( x + 7 ) + ( x - 9 ) ( x + 7 )(x−9)(x+7)+(x−9)(x+7)