Question 1

Perform the indicated operations.
-$\frac { 7 } { 9 x } + \frac { 5 } { 9 x }$

Accepted Answer

A)  $\frac { 12 } { 18 x }$ 
B)  1 
C)  $\frac { 3 } { 4 x }$ 
D)  $\frac { 4 } { 3 x }$ 
A)  $\frac { 12 } { 18 x }$ 
B)  1 
C)  $\frac { 3 } { 4 x }$ 
D)  $\frac { 4 } { 3 x }$

Question 2

Decide whether the expression has been simplified correctly.
-$$x ^ { 7 } \cdot x ^ { 2 } = x ^ { 14 }$$

Accepted Answer

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

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 175 x ^ { 2 } }$

Accepted Answer

A)  $7 x ^ { 2 } \sqrt { 5 }$ 
B)  $5 \sqrt { 7 x }$ 
C)  $5x \sqrt { 7 }$ 
D)  $175 \mathrm { x }$ 
A)  $7 x ^ { 2 } \sqrt { 5 }$ 
B)  $5 \sqrt { 7 x }$ 
C)  $5x \sqrt { 7 }$ 
D)  $175 \mathrm { x }$

Question 4

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| - 7 | = - | 7 |$$

Accepted Answer

A)  True 
B)  False; $| - 7 | = - ( - 7 ) = 7$ 
A)  True 
B)  False; $| - 7 | = - ( - 7 ) = 7$

Question 5

Evaluate the expression.
-$1296^{1 / 4}$

Accepted Answer

A)  6 
B)  7776 
C)  24 
D)  144 
A)  6 
B)  7776 
C)  24 
D)  144

Question 6

Solve the problem.
-The cost of manufacturing clocks is given by $c = 49 ( n + 9 ) ^ { 1 / 2 }$, where $c$ is the cost in dollars and $n$ is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $\$ 49$ 
B)  $\$ 147$ 
C)  $\$ 441$ 
D)  $\$ 21$ 
A)  $\$ 49$ 
B)  $\$ 147$ 
C)  $\$ 441$ 
D)  $\$ 21$

Question 7

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\left( \frac { 1 } { 3 } \right) ^ { - 4 }$$

Accepted Answer

A)  81 
B)  $- 81$ 
C)  $\frac { 1 } { 81 }$ 
D)  $- \frac { 1 } { 81 }$ 
A)  81 
B)  $- 81$ 
C)  $\frac { 1 } { 81 }$ 
D)  $- \frac { 1 } { 81 }$

Question 8

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { x ^ { 6 } } { x ^ { - 8 } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $\frac { 1 } { x ^ { 14 } }$ 
C)  $x ^ { 14 }$ 
D)  $- x ^ { 2 }$ 
A)  $\frac { 1 } { x ^ { 2 } }$ 
B)  $\frac { 1 } { x ^ { 14 } }$ 
C)  $x ^ { 14 }$ 
D)  $- x ^ { 2 }$

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
-$6 \sqrt { 32 x ^ { 2 } } - 3 \sqrt { 18 x ^ { 2 } } - \sqrt { 2 x ^ { 2 } }$

Accepted Answer

A)  $2 x \sqrt { 14 }$ 
B)  $14 x \sqrt { 2 }$ 
C)  $3 x \sqrt { 14 }$ 
D)  $15 x \sqrt { 2 }$ 
A)  $2 x \sqrt { 14 }$ 
B)  $14 x \sqrt { 2 }$ 
C)  $3 x \sqrt { 14 }$ 
D)  $15 x \sqrt { 2 }$

Question 10

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 24 a ^ { - 4 } b ^ { 4 } } { 8 a ^ { - 11 } b ^ { 8 } }$

Accepted Answer

A)  $- 3 a b ^ { 2 }$ 
B)  $\frac { 3 a ^ { 7 } } { b ^ { 4 } }$ 
C)  $\frac { 3 b ^ { 5 } } { a ^ { 7 } }$ 
D)  $- \frac { a ^ { 6 } } { 3 b ^ { 5 } }$ 
A)  $- 3 a b ^ { 2 }$ 
B)  $\frac { 3 a ^ { 7 } } { b ^ { 4 } }$ 
C)  $\frac { 3 b ^ { 5 } } { a ^ { 7 } }$ 
D)  $- \frac { a ^ { 6 } } { 3 b ^ { 5 } }$

Question 11

Perform the indicated operations.
-$$\frac { - 49 x } { 2 ( 7 x + 1 ) } + \frac { 1 } { 2 x ( 7 x + 1 ) } - \frac { 11 } { x }$$

Accepted Answer

A)  $\frac { - 49 x ^ { 2 } - 154 x - 21 } { 2 x }$ 
B)  $- \frac { 7 ( x + 3 ) } { 14 x ^ { 2 } + 2 x }$ 
C)  $- \frac { 7 ( x + 3 ) } { 2 x }$ 
D)  $\frac { - 49 x ^ { 2 } - 154 x - 21 } { 14 x ^ { 2 } + 2 x }$ 
A)  $\frac { - 49 x ^ { 2 } - 154 x - 21 } { 2 x }$ 
B)  $- \frac { 7 ( x + 3 ) } { 14 x ^ { 2 } + 2 x }$ 
C)  $- \frac { 7 ( x + 3 ) } { 2 x }$ 
D)  $\frac { - 49 x ^ { 2 } - 154 x - 21 } { 14 x ^ { 2 } + 2 x }$

Question 12

Calculate the value mentally.
-$\frac { 12 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }$

Accepted Answer

A)  2 
B)  none of these 
C)  9 
D)  4 
A)  2 
B)  none of these 
C)  9 
D)  4

Question 13

Factor the trinomial, if possible.
-$- 3 x ^ { 2 } - 18 x + 48$

Accepted Answer

A)  $- 3 ( x + 2 ) ( x - 8 )$ 
B)  $3 ( x - 2 ) ( x + 8 )$ 
C)  $- 3 ( x + 2 ) ( x + 8 )$ 
D)  $- 3 ( x - 2 ) ( x + 8 )$ 
A)  $- 3 ( x + 2 ) ( x - 8 )$ 
B)  $3 ( x - 2 ) ( x + 8 )$ 
C)  $- 3 ( x + 2 ) ( x + 8 )$ 
D)  $- 3 ( x - 2 ) ( x + 8 )$

Question 14

Evaluate the expression.
-$$\left( - \frac { 64 } { 81 } \right) ^ { - 1 / 2 }$$

Accepted Answer

A)  $\frac { 8 } { 9 }$ 
B)  not a real number 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { 32 } { 81 }$ 
A)  $\frac { 8 } { 9 }$ 
B)  not a real number 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { 32 } { 81 }$

Question 15

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 15 } \cdot \sqrt { 48 }$

Accepted Answer

A)  $20 \sqrt { 3 }$ 
B)  $- 20 \sqrt { 3 }$ 
C)  $12 \sqrt { 5 }$ 
D)  $- 12 \sqrt { 5 }$ 
A)  $20 \sqrt { 3 }$ 
B)  $- 20 \sqrt { 3 }$ 
C)  $12 \sqrt { 5 }$ 
D)  $- 12 \sqrt { 5 }$

Question 16

Find the product. Assume variables represent positive real numbers.
-$\left( \mathrm { m } ^ { 1 / 4 } + \mathrm { m } ^ { - 1 / 4 } \right) \left( \mathrm { m } ^ { - 1 / 4 } - \mathrm { m } ^ { 1 / 4 } \right)$

Accepted Answer

A)  $m - m ^ { 1 / 2 } + m ^ { - 1 / 2 } - 1$ 
B)  $- m ^ { 1 / 2 } + m ^ { - 1 / 2 }$ 
C)  $m 1 / 2 - m ^ { - 1 / 2 }$ 
D)  $1 - \mathrm { m } ^ { 1 / 2 } + \mathrm { m } ^ { - 1 / 2 } - \mathrm { m }$ 
A)  $m - m ^ { 1 / 2 } + m ^ { - 1 / 2 } - 1$ 
B)  $- m ^ { 1 / 2 } + m ^ { - 1 / 2 }$ 
C)  $m 1 / 2 - m ^ { - 1 / 2 }$ 
D)  $1 - \mathrm { m } ^ { 1 / 2 } + \mathrm { m } ^ { - 1 / 2 } - \mathrm { m }$

Question 17

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 2 a ^ { 5 } b ^ { 4 } \right) \left( - 3 a ^ { 6 } b ^ { 3 } \right)$

Accepted Answer

A)  $- 6 a ^ { 11 } b ^ { 7 }$ 
B)  $- 6 a ^ { 30 } b ^ 6$ 
C)  $6 \mathrm { a } ^ { 11 } \mathrm {~b} ^ { 8 }$ 
D)  $6 \mathrm { a } ^ { 29 } \mathrm {~b} 6$ 
A)  $- 6 a ^ { 11 } b ^ { 7 }$ 
B)  $- 6 a ^ { 30 } b ^ 6$ 
C)  $6 \mathrm { a } ^ { 11 } \mathrm {~b} ^ { 8 }$ 
D)  $6 \mathrm { a } ^ { 29 } \mathrm {~b} 6$

Question 18

Evaluate the expression.
-$$10 + 29 \cdot 7 + 11$$

Accepted Answer

A)  224 
B)  284 
C)  57 
D)  702 
A)  224 
B)  284 
C)  57 
D)  702

Question 19

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$$\frac { 5 } { 2 } ( 2 y )$$

Accepted Answer

A)  -5y 
B)  7y 
C)  5y 
D)  10y 
A)  -5y 
B)  7y 
C)  5y 
D)  10y

Question 20

Evaluate the expression.
-$256 ^ { 5 / 4 }$

Accepted Answer

A)  1024 
B)  262,144 
C)  16,384 
D)  65,536 
A)  1024 
B)  262,144 
C)  16,384 
D)  65,536

Perform the indicated operations. - $\frac { 7 } { 9 x } + \frac { 5 } { 9 x }$

Decide whether the expression has been simplified correctly. - $x ^ { 7 } \cdot x ^ { 2 } = x ^ { 14 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 175 x ^ { 2 } }$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 7 | = - | 7 |$

Evaluate the expression. - $1296^{1 / 4}$

Solve the problem. -The cost of manufacturing clocks is given by $c = 49 ( n + 9 ) ^ { 1 / 2 }$ , where $c$ is the cost in dollars and $n$ is the number produced. What is the cost when no clocks are produced?

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\left( \frac { 1 } { 3 } \right) ^ { - 4 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 6 } } { x ^ { - 8 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $6 \sqrt { 32 x ^ { 2 } } - 3 \sqrt { 18 x ^ { 2 } } - \sqrt { 2 x ^ { 2 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 24 a ^ { - 4 } b ^ { 4 } } { 8 a ^ { - 11 } b ^ { 8 } }$

Perform the indicated operations. - $\frac { - 49 x } { 2 ( 7 x + 1 ) } + \frac { 1 } { 2 x ( 7 x + 1 ) } - \frac { 11 } { x }$

Calculate the value mentally. - $\frac { 12 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }$

Factor the trinomial, if possible. - $- 3 x ^ { 2 } - 18 x + 48$

Evaluate the expression. - $\left( - \frac { 64 } { 81 } \right) ^ { - 1 / 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 15 } \cdot \sqrt { 48 }$

Find the product. Assume variables represent positive real numbers. - $\left( \mathrm { m } ^ { 1 / 4 } + \mathrm { m } ^ { - 1 / 4 } \right) \left( \mathrm { m } ^ { - 1 / 4 } - \mathrm { m } ^ { 1 / 4 } \right)$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 2 a ^ { 5 } b ^ { 4 } \right) \left( - 3 a ^ { 6 } b ^ { 3 } \right)$

Evaluate the expression. - $10 + 29 \cdot 7 + 11$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 5 } { 2 } ( 2 y )$

Evaluate the expression. - $256 ^ { 5 / 4 }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Applications of Trigonometry

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Exam 12: Review of Basic Concepts

Perform the indicated operations. - 79x+59x\frac { 7 } { 9 x } + \frac { 5 } { 9 x }9x7​+9x5​

Decide whether the expression has been simplified correctly. - x7⋅x2=x14x ^ { 7 } \cdot x ^ { 2 } = x ^ { 14 }x7⋅x2=x14

Simplify the expression. Assume all variables represent positive real numbers. - 175x2\sqrt { 175 x ^ { 2 } }175x2​

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−7∣=−∣7∣| - 7 | = - | 7 |∣−7∣=−∣7∣

Evaluate the expression. - 12961/41296^{1 / 4}12961/4

Solve the problem. -The cost of manufacturing clocks is given by c=49(n+9)1/2c = 49 ( n + 9 ) ^ { 1 / 2 }c=49(n+9)1/2 , where ccc is the cost in dollars and nnn is the number produced. What is the cost when no clocks are produced?

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (13)−4\left( \frac { 1 } { 3 } \right) ^ { - 4 }(31​)−4

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x6x−8\frac { x ^ { 6 } } { x ^ { - 8 } }x−8x6​

Simplify the expression. Assume all variables represent positive real numbers. - 632x2−318x2−2x26 \sqrt { 32 x ^ { 2 } } - 3 \sqrt { 18 x ^ { 2 } } - \sqrt { 2 x ^ { 2 } }632x2​−318x2​−2x2​

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 24a−4b48a−11b8\frac { 24 a ^ { - 4 } b ^ { 4 } } { 8 a ^ { - 11 } b ^ { 8 } }8a−11b824a−4b4​

Perform the indicated operations. - −49x2(7x+1)+12x(7x+1)−11x\frac { - 49 x } { 2 ( 7 x + 1 ) } + \frac { 1 } { 2 x ( 7 x + 1 ) } - \frac { 11 } { x }2(7x+1)−49x​+2x(7x+1)1​−x11​

Calculate the value mentally. - 121/231/2\frac { 12 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }31/2121/2​

Factor the trinomial, if possible. - −3x2−18x+48- 3 x ^ { 2 } - 18 x + 48−3x2−18x+48

Evaluate the expression. - (−6481)−1/2\left( - \frac { 64 } { 81 } \right) ^ { - 1 / 2 }(−8164​)−1/2

Simplify the expression. Assume all variables represent positive real numbers. - 15⋅48\sqrt { 15 } \cdot \sqrt { 48 }15​⋅48​

Find the product. Assume variables represent positive real numbers. - (m1/4+m−1/4)(m−1/4−m1/4)\left( \mathrm { m } ^ { 1 / 4 } + \mathrm { m } ^ { - 1 / 4 } \right) \left( \mathrm { m } ^ { - 1 / 4 } - \mathrm { m } ^ { 1 / 4 } \right)(m1/4+m−1/4)(m−1/4−m1/4)

Simplify the expression. Assume all variables represent nonzero real numbers. - (2a5b4)(−3a6b3)\left( 2 a ^ { 5 } b ^ { 4 } \right) \left( - 3 a ^ { 6 } b ^ { 3 } \right)(2a5b4)(−3a6b3)

Evaluate the expression. - 10+29⋅7+1110 + 29 \cdot 7 + 1110+29⋅7+11

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 52(2y)\frac { 5 } { 2 } ( 2 y )25​(2y)

Evaluate the expression. - 2565/4256 ^ { 5 / 4 }2565/4