Question 1

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$11^0$

Accepted Answer

A)  1 
B)  0 
C)  11 
D)  -1 
A)  1 
B)  0 
C)  11 
D)  -1

Question 2

Factor out the greatest common factor. Simplify the factors, if possible.
-$$5 t ^ { 2 } - 10 t - 25$$

Accepted Answer

A)  $5 t \left( t ^ { 2 } - 2 t - 5 \right)$ 
B)  $5 \left( t ^ { 2 } - 2 t - 5 \right)$ 
C)  $5 \left( t ^ { 2 } - 5 t - 20 \right)$ 
D)  $5 \left( t ^ { 2 } - 10 t - 25 \right)$ 
A)  $5 t \left( t ^ { 2 } - 2 t - 5 \right)$ 
B)  $5 \left( t ^ { 2 } - 2 t - 5 \right)$ 
C)  $5 \left( t ^ { 2 } - 5 t - 20 \right)$ 
D)  $5 \left( t ^ { 2 } - 10 t - 25 \right)$

Question 3

Factor the trinomial, if possible.
-$$72 x ^ { 2 } + 42 x y + 6 y ^ { 2 }$$

Accepted Answer

A)  $6 ( 3 x - y ) ( 4 x - y )$ 
B)  $( 18 x + 6 y ) ( 4 x + y )$ 
C)  $( 3 x + y ) ( 6 x + 3 y )$ 
D)  $6 ( 3 x + y ) ( 4 x + y )$ 
A)  $6 ( 3 x - y ) ( 4 x - y )$ 
B)  $( 18 x + 6 y ) ( 4 x + y )$ 
C)  $( 3 x + y ) ( 6 x + 3 y )$ 
D)  $6 ( 3 x + y ) ( 4 x + y )$

Question 4

Round to two decimal places unless otherwise indicated.
If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $y =$ $\frac { 112,500 } { x + 225 }$. What is the cost per ton for $x = 10$ ?

Accepted Answer

A)  $\$ 50.00$ 
B)  $\$ 478.72$ 
C)  $\$ 11250.00$ 
D)  $\$ 11025.00$ 
A)  $\$ 50.00$ 
B)  $\$ 478.72$ 
C)  $\$ 11250.00$ 
D)  $\$ 11025.00$

Question 5

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-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 30,000 feet? Round your answer to the nearest tenth mile, if necessary.

Accepted Answer

A)  191.3 mi 
B)  211.3 mi 
C)  18,300 mi 
D)  1830 mi 
A)  191.3 mi 
B)  211.3 mi 
C)  18,300 mi 
D)  1830 mi

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )$

Accepted Answer

A)  $6 - 2 \sqrt { 4 }$ 
B)  $- 10$ 
C)  22 
D)  2 
A)  $6 - 2 \sqrt { 4 }$ 
B)  $- 10$ 
C)  22 
D)  2

Question 7

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

Accepted Answer

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

Question 8

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 6 ] { ( - 7 ) ^ { 6 } }$$

Accepted Answer

A)  $- 7$ 
B)  49 
C)  not a real number 
D)  7 
A)  $- 7$ 
B)  49 
C)  not a real number 
D)  7

Question 9

Evaluate the expression.
-$$- \left( \frac { 36 } { 49 } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  not a real number 
B)  $- \frac { 18 } { 49 }$ 
C)  $\frac { 7 } { 6 }$ 
D)  $- \frac { 6 } { 7 }$ 
A)  not a real number 
B)  $- \frac { 18 } { 49 }$ 
C)  $\frac { 7 } { 6 }$ 
D)  $- \frac { 6 } { 7 }$

Question 10

Factor by any method.
-$( 2 x + 1 ) ^ { 2 } - y ^ { 2 }$

Accepted Answer

A)  $( 2 x - 1 + y ) ( 2 x - 1 - y )$ 
B)  prime 
C)  $( 2 x + 1 + y ) ( 2 x - 1 - y )$ 
D)  $( 2 x + 1 + y ) ( 2 x + 1 - y )$ 
A)  $( 2 x - 1 + y ) ( 2 x - 1 - y )$ 
B)  prime 
C)  $( 2 x + 1 + y ) ( 2 x - 1 - y )$ 
D)  $( 2 x + 1 + y ) ( 2 x + 1 - y )$

Question 11

Solve the problem.
-$$\left( 3 x ^ { 2 } + 2 y \right) \left( - 4 x ^ { 2 } - 7 y + z \right)$$

Accepted Answer

A)  $- 12 x ^ { 2 } - 29 x y + 3 x ^ { 2 } z - 14 y ^ { 2 } + 2 z$ 
B)  $- 12 x ^ { 4 } - 29 x ^ { 2 } y - 14 y ^ { 4 } + 3 x ^ { 2 } y z$ 
C)  $- 12 x ^ { 4 } - 29 x ^ { 2 } y ^ { 2 } - 14 y ^ { 2 }$ 
D)  $- 12 x ^ { 4 } - 29 x ^ { 2 } y + 3 x ^ { 2 } z - 14 y ^ { 2 } + 2 y z$ 
A)  $- 12 x ^ { 2 } - 29 x y + 3 x ^ { 2 } z - 14 y ^ { 2 } + 2 z$ 
B)  $- 12 x ^ { 4 } - 29 x ^ { 2 } y - 14 y ^ { 4 } + 3 x ^ { 2 } y z$ 
C)  $- 12 x ^ { 4 } - 29 x ^ { 2 } y ^ { 2 } - 14 y ^ { 2 }$ 
D)  $- 12 x ^ { 4 } - 29 x ^ { 2 } y + 3 x ^ { 2 } z - 14 y ^ { 2 } + 2 y z$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }$$

Accepted Answer

A)  $\frac { 2 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 4 \sqrt { 3 } } { 3 }$ 
C)  $- \frac { \sqrt { 45 } } { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } } { 9 }$ 
A)  $\frac { 2 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 4 \sqrt { 3 } } { 3 }$ 
C)  $- \frac { \sqrt { 45 } } { 3 }$ 
D)  $\frac { 2 \sqrt { 3 } } { 9 }$

Question 13

Factor, using the given factor. Assume all variables represent positive real numbers.
-$( q + 6 ) ^ { - 3 / 17 } + ( q + 6 ) ^ { - 1 / 17 } + ( q + 6 ) ^ { 1 / 17 } ; \quad ( q + 6 ) ^ { - 3 / 17 }$

Accepted Answer

A)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { 1 / 17 } + ( q + 6 ) ^ { 3 / 17 } \right]$ 
B)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { - 2 / 17 } + ( q + 6 ) ^ { - 4 / 17 } \right]$ 
C)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { 2 / 17 } + ( q + 6 ) ^ { 4 / 17 } \right]$ 
D)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { 4 / 17 } + ( q + 6 ) ^ { 6 / 17 } \right]$ 
A)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { 1 / 17 } + ( q + 6 ) ^ { 3 / 17 } \right]$ 
B)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { - 2 / 17 } + ( q + 6 ) ^ { - 4 / 17 } \right]$ 
C)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { 2 / 17 } + ( q + 6 ) ^ { 4 / 17 } \right]$ 
D)  $( q + 6 ) ^ { - 3 / 17 } \left[ 1 + ( q + 6 ) ^ { 4 / 17 } + ( q + 6 ) ^ { 6 / 17 } \right]$

Question 14

Write in radical form. Assume all variables represent positive real numbers.
-$x^{1 / 7}$

Accepted Answer

A)  $\sqrt { x ^ { 7 } }$ 
B)  $\sqrt [ 7 ] { \mathrm { x } }$ 
C)  $\frac { 1 } { \sqrt [ 7 ] { x } }$ 
D)  $x ^ { - 7 }$ 
A)  $\sqrt { x ^ { 7 } }$ 
B)  $\sqrt [ 7 ] { \mathrm { x } }$ 
C)  $\frac { 1 } { \sqrt [ 7 ] { x } }$ 
D)  $x ^ { - 7 }$

Question 15

Factor the polynomial by substitution.
-$$9 z ^ { 6 } + 6 z ^ { 3 } - 8$$

Accepted Answer

A)  $\left( 3 z ^ { 3 } + 2 \right) \left( 3 z ^ { 3 } - 4 \right)$ 
B)  $\left( 3 z ^ { 3 } + 4 \right) \left( 3 z ^ { 3 } - 2 \right)$ 
C)  $\left( 3 z ^ { 3 } + 1 \right) \left( 3 z ^ { 3 } - 8 \right)$ 
D)  $9 \left( z ^ { 3 } - 2 \right) \left( z ^ { 3 } + 4 \right)$ 
A)  $\left( 3 z ^ { 3 } + 2 \right) \left( 3 z ^ { 3 } - 4 \right)$ 
B)  $\left( 3 z ^ { 3 } + 4 \right) \left( 3 z ^ { 3 } - 2 \right)$ 
C)  $\left( 3 z ^ { 3 } + 1 \right) \left( 3 z ^ { 3 } - 8 \right)$ 
D)  $9 \left( z ^ { 3 } - 2 \right) \left( z ^ { 3 } + 4 \right)$

Question 16

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-A manufacturer's cost is given b $$C = 500 n ^ { 1 / 3 } + 1200$$ , where C is the cost in dollars and n is the number of parts produced. Find the cost when 729 parts are produced.

Accepted Answer

A)  $14,700 
B)  $56 
C)  $5700 
D)  $3450 
A)  $14,700 
B)  $56 
C)  $5700 
D)  $3450

Question 17

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$$

Accepted Answer

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

Question 18

Decide whether the expression has been simplified correctly.
-$5 ^ { 0 } x = x$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Question 19

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }$$

Accepted Answer

A)  $\frac { 1 } { 6^{10} }$ 
B)  $- 3^{10}$ 
C)  $\frac { 1 } { 3 ^ { 10 } }$ 
D)  $\frac { 1 } { 3 ^ { 24 } }$ 
A)  $\frac { 1 } { 6^{10} }$ 
B)  $- 3^{10}$ 
C)  $\frac { 1 } { 3 ^ { 10 } }$ 
D)  $\frac { 1 } { 3 ^ { 24 } }$

Question 20

Factor, using the given factor. Assume all variables represent positive real numbers.
-$14 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }$

Accepted Answer

A)  $s ^ { 1 / 7 } \left( 14 s ^ { 3 / 7 } - 8 ^ { 3 / 8 } \right)$ 
B)  $\mathrm { s } ^ { - 2 / 7 } \left( 14 \mathrm {~s} ^ { 3 / 7 } - 8 \right)$ 
C)  $s ^ { - 2 / 7 } \left( 14 s ^ { 3 / 7 } - 8 s \right)$ 
D)  $s ^ { 1 / 3 } \left( 14 - 8 s ^ { 3 / 8 } \right)$ 
A)  $s ^ { 1 / 7 } \left( 14 s ^ { 3 / 7 } - 8 ^ { 3 / 8 } \right)$ 
B)  $\mathrm { s } ^ { - 2 / 7 } \left( 14 \mathrm {~s} ^ { 3 / 7 } - 8 \right)$ 
C)  $s ^ { - 2 / 7 } \left( 14 s ^ { 3 / 7 } - 8 s \right)$ 
D)  $s ^ { 1 / 3 } \left( 14 - 8 s ^ { 3 / 8 } \right)$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $11^0$

Factor out the greatest common factor. Simplify the factors, if possible. - $5 t ^ { 2 } - 10 t - 25$

Factor the trinomial, if possible. - $72 x ^ { 2 } + 42 x y + 6 y ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )$

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

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 6 ] { ( - 7 ) ^ { 6 } }$

Evaluate the expression. - $- \left( \frac { 36 } { 49 } \right) ^ { 1 / 2 }$

Factor by any method. - $( 2 x + 1 ) ^ { 2 } - y ^ { 2 }$

Solve the problem. - $\left( 3 x ^ { 2 } + 2 y \right) \left( - 4 x ^ { 2 } - 7 y + z \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }$

Factor, using the given factor. Assume all variables represent positive real numbers. - $( q + 6 ) ^ { - 3 / 17 } + ( q + 6 ) ^ { - 1 / 17 } + ( q + 6 ) ^ { 1 / 17 } ; \quad ( q + 6 ) ^ { - 3 / 17 }$

Write in radical form. Assume all variables represent positive real numbers. - $x^{1 / 7}$

Factor the polynomial by substitution. - $9 z ^ { 6 } + 6 z ^ { 3 } - 8$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -A manufacturer's cost is given b $C = 500 n ^ { 1 / 3 } + 1200$ , where C is the cost in dollars and n is the number of parts produced. Find the cost when 729 parts are produced.

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$

Decide whether the expression has been simplified correctly. - $5 ^ { 0 } x = x$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }$

Factor, using the given factor. Assume all variables represent positive real numbers. - $14 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }$

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Exam 1: Review of Basic Concepts

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 11011^0110

Factor out the greatest common factor. Simplify the factors, if possible. - 5t2−10t−255 t ^ { 2 } - 10 t - 255t2−10t−25

Factor the trinomial, if possible. - 72x2+42xy+6y272 x ^ { 2 } + 42 x y + 6 y ^ { 2 }72x2+42xy+6y2

Simplify the expression. Assume all variables represent positive real numbers. - (6+4)(6−4)( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )(6​+4)(6​−4)

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

Simplify the expression. Assume all variables represent positive real numbers. - (−7)66\sqrt [ 6 ] { ( - 7 ) ^ { 6 } }6(−7)6​

Evaluate the expression. - −(3649)1/2- \left( \frac { 36 } { 49 } \right) ^ { 1 / 2 }−(4936​)1/2

Factor by any method. - (2x+1)2−y2( 2 x + 1 ) ^ { 2 } - y ^ { 2 }(2x+1)2−y2

Solve the problem. - (3x2+2y)(−4x2−7y+z)\left( 3 x ^ { 2 } + 2 y \right) \left( - 4 x ^ { 2 } - 7 y + z \right)(3x2+2y)(−4x2−7y+z)

Simplify the expression. Assume all variables represent positive real numbers. - 483−333+39\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }348​​−333​​+9​3​​

Factor, using the given factor. Assume all variables represent positive real numbers. - (q+6)−3/17+(q+6)−1/17+(q+6)1/17;(q+6)−3/17( q + 6 ) ^ { - 3 / 17 } + ( q + 6 ) ^ { - 1 / 17 } + ( q + 6 ) ^ { 1 / 17 } ; \quad ( q + 6 ) ^ { - 3 / 17 }(q+6)−3/17+(q+6)−1/17+(q+6)1/17;(q+6)−3/17

Write in radical form. Assume all variables represent positive real numbers. - x1/7x^{1 / 7}x1/7

Factor the polynomial by substitution. - 9z6+6z3−89 z ^ { 6 } + 6 z ^ { 3 } - 89z6+6z3−8

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 1h(1(x+h)2+2−1x2+2)\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)h1​((x+h)2+21​−x2+21​)

Decide whether the expression has been simplified correctly. - 50x=x5 ^ { 0 } x = x50x=x

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 3−634\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }343−6​

Factor, using the given factor. Assume all variables represent positive real numbers. - 14s1/7−8s−2/7;s−2/714 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }14s1/7−8s−2/7;s−2/7