Question 1

Simplify the expression. $\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }$

Accepted Answer

A)  $\quad 5 | y |$ 
B)  $\quad 25 | y |$ 
C)  $\quad 5 \left| y ^ { 2 } \right|$ 
D)  $5 y$ 
E)  $\quad 5 y ^ { 2 }$ 
A)  $\quad 5 | y |$ 
B)  $\quad 25 | y |$ 
C)  $\quad 5 \left| y ^ { 2 } \right|$ 
D)  $5 y$ 
E)  $\quad 5 y ^ { 2 }$

Question 2

Give the degree of the polynomial. $\sqrt { 576 }$

Accepted Answer

A)  0 
B)  No defined degree 
C)  $1 / 2$ 
D)  This is not a polynomial 
A)  0 
B)  No defined degree 
C)  $1 / 2$ 
D)  This is not a polynomial

Question 3

Give the degree of the polynomial. $\sqrt { 127 }$

Accepted Answer

A)  $1 / 2$ 
B)  No defined degree 
C)  This is not a polynomial 
D)  0 
A)  $1 / 2$ 
B)  No defined degree 
C)  This is not a polynomial 
D)  0

Question 4

We can often multiply and divide radicals with different indexes.For example: $$\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$$
Use this idea to write the following expression as a single radical.
$\frac { \sqrt [ 6 ] { 4 } } { \sqrt { 5 } }$

Accepted Answer

A)  $\quad \frac { \sqrt [ 6 ] { 500 } } { 9 }$ 
B)  $\frac { \sqrt [ 6 ] { 500 } } { 5 }$ 
C)  $\frac { \sqrt [ 6 ] { 500 } } { 4 }$ 
D)  $\frac { \sqrt [ 7 ] { 500 } } { 5 }$ 
A)  $\quad \frac { \sqrt [ 6 ] { 500 } } { 9 }$ 
B)  $\frac { \sqrt [ 6 ] { 500 } } { 5 }$ 
C)  $\frac { \sqrt [ 6 ] { 500 } } { 4 }$ 
D)  $\frac { \sqrt [ 7 ] { 500 } } { 5 }$

Question 5

Simplify the expression. $( - 4 x ) ^ { 0 }$
Write the answer without using exponents.

Accepted Answer

A)  1 
B)  4
$\begin{array} { l l } \text { c. } & - 4 \ \text { d. } & - 1 \end{array}$ 
A)  1 
B)  4
$\begin{array} { l l } \text { c. } & - 4 \ \text { d. } & - 1 \end{array}$

Question 6

Express the number -187,000,000 in scientific notation.

Accepted Answer

A) $- 1.87 \times 10 ^ { 8 }$ 
B)  $- 1.87 \times 10 ^ { 7 }$ 
C)  $- 1.87 \times 10 ^ { 9 }$ 
D)  $- 18.7 \times 10 ^ { 9 }$ 
A) $- 1.87 \times 10 ^ { 8 }$ 
B)  $- 1.87 \times 10 ^ { 7 }$ 
C)  $- 1.87 \times 10 ^ { 9 }$ 
D)  $- 18.7 \times 10 ^ { 9 }$

Question 7

Simplify the expression. $$\left( - \frac { 343 x ^ { 9 } } { 125 y ^ { 3 } } \right) ^ { 1 / 3 }$$

Accepted Answer

A)  $ \quad \frac{7 x^{3}}{5 y} $ 
B)  $ -\frac{7 x^{3}}{5 y} $ 
C)  $ -\frac{7 x^{3}}{5 y^{2}} $ 
D)  $ \quad \frac{7 x^{4}}{5 y} $ 
A)  $ \quad \frac{7 x^{3}}{5 y} $ 
B)  $ -\frac{7 x^{3}}{5 y} $ 
C)  $ -\frac{7 x^{3}}{5 y^{2}} $ 
D)  $ \quad \frac{7 x^{4}}{5 y} $

Question 8

Identify the correct union of intervals for the inequality. $x \leq - 18$ or $x > 4$

Accepted Answer

A)  $\quad ( - \infty , - 18 ] \cup ( 4 , \infty )$ 
B)  $\quad ( - \infty , - 18 ) \cup ( 4 , \infty )$ 
C)  $\quad ( - \infty , - 18 ] \cup ( 4 , \infty ]$ 
D)  $\quad ( - \infty , - 18 ] \cup [ 4 , \infty )$ 
E)  $( - \infty , - 18 ) \cup [ 4 , \infty )$ 
A)  $\quad ( - \infty , - 18 ] \cup ( 4 , \infty )$ 
B)  $\quad ( - \infty , - 18 ) \cup ( 4 , \infty )$ 
C)  $\quad ( - \infty , - 18 ] \cup ( 4 , \infty ]$ 
D)  $\quad ( - \infty , - 18 ] \cup [ 4 , \infty )$ 
E)  $( - \infty , - 18 ) \cup [ 4 , \infty )$

Question 9

We can often multiply and divide radicals with different indexes.For example: $$\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$$
Use this idea to write the following expression as a single radical.
$\sqrt { 5 } \sqrt [ 3 ] { 5 }$

Accepted Answer

A)  $\sqrt [ 3 ] { 3125 }$ 
B)  $\sqrt [ 6 ] { 5 }$ 
C)  $\sqrt [ 6 ] { 3125 }$ 
D)  $\sqrt { 3125 }$ 
E)  $\sqrt [ 6 ] { 625 }$ 
A)  $\sqrt [ 3 ] { 3125 }$ 
B)  $\sqrt [ 6 ] { 5 }$ 
C)  $\sqrt [ 6 ] { 3125 }$ 
D)  $\sqrt { 3125 }$ 
E)  $\sqrt [ 6 ] { 625 }$

Question 10

Perform the operation and simplify. $( a - 8 ) ^ { 2 }$

Accepted Answer

A)  $\quad a ^ { 2 } - 8 a + 64$ 
B)  $\quad a ^ { 2 } - 16 a + 64$ 
C)  $\quad a ^ { 2 } - 64$ 
D)  $\quad a ^ { 2 } + 64$ 
E)  $\quad a ^ { 2 } + 16 a + 64$ 
A)  $\quad a ^ { 2 } - 8 a + 64$ 
B)  $\quad a ^ { 2 } - 16 a + 64$ 
C)  $\quad a ^ { 2 } - 64$ 
D)  $\quad a ^ { 2 } + 64$ 
E)  $\quad a ^ { 2 } + 16 a + 64$

Question 11

Simplify the expression. $$\frac { \left( 8 ^ { - 2 } z ^ { - 5 } y \right) ^ { - 1 } } { \left( 5 y ^ { 5 } z ^ { - 1 } \right) ^ { 3 } \left( 5 y z ^ { - 1 } \right) ^ { - 2 } }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }$ 
B)  $\frac { 5 y ^ { 14 } } { 64 z ^ { 6 } }$ 
C)  $\quad \frac { 64 z ^ { 14 } } { 5 y ^ { 6 } }$ 
D)  $\frac { 8 z ^ { 5 } } { 5 y ^ { 15 } }$ 
A)  $\quad \frac { 64 z ^ { 6 } } { 5 y ^ { 14 } }$ 
B)  $\frac { 5 y ^ { 14 } } { 64 z ^ { 6 } }$ 
C)  $\quad \frac { 64 z ^ { 14 } } { 5 y ^ { 6 } }$ 
D)  $\frac { 8 z ^ { 5 } } { 5 y ^ { 15 } }$

Question 12

Simplify the expression. $( - 13 x ) ^ { 0 }$
Write the answer without using exponents.

Accepted Answer

A)  1 
B)  13 
C)  $- 13$ 
D)  $- 1$ 
A)  1 
B)  13 
C)  $- 13$ 
D)  $- 1$

Question 13

Simplify the expression. $- 8 ^ { 4 / 3 }$

Accepted Answer

A)  $- 10.6667$ 
B)  19 
C)  $- 32$ 
D)  $- 48$ 
E)  $- 18$
F) $- 16$ 
A)  $- 10.6667$ 
B)  19 
C)  $- 32$ 
D)  $- 48$ 
E)  $- 18$
F) $- 16$

Question 14

Simplify the expression. $$\left( \frac { 8 x ^ { - 4 } y ^ { 5 } z ^ { - 8 } } { 32 x ^ { 4 } y ^ { 12 } z ^ { - 13 } } \right) ^ { 3 }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $\quad \frac { z ^ { 5 } } { 4 x ^ { 8 } y ^ { 7 } }$ 
B)  $\quad \frac { z ^ { 15 } } { 64 x ^ { 24 } y ^ { 21 } }$ 
C)  $\quad \frac { z ^ { 15 } } { 64 x ^ { 21 } y ^ { 24 } }$ 
D)  $\frac { z ^ { 15 } } { 64 x ^ { - 24 } y ^ { - 21 } }$ 
E)  $\frac { z ^ { 5 } } { 4 x ^ { 24 } y ^ { 21 } }$ 
A)  $\quad \frac { z ^ { 5 } } { 4 x ^ { 8 } y ^ { 7 } }$ 
B)  $\quad \frac { z ^ { 15 } } { 64 x ^ { 24 } y ^ { 21 } }$ 
C)  $\quad \frac { z ^ { 15 } } { 64 x ^ { 21 } y ^ { 24 } }$ 
D)  $\frac { z ^ { 15 } } { 64 x ^ { - 24 } y ^ { - 21 } }$ 
E)  $\frac { z ^ { 5 } } { 4 x ^ { 24 } y ^ { 21 } }$

Question 15

Simplify the expression. $$\left( x ^ { 3 } \right) ^ { 3 } \left( x ^ { 3 } \right) ^ { 2 }$$

Accepted Answer

A)  $x ^ { 11 }$ 
B)  $x ^ { - 1 }$ 
C)  $x ^ { 10 }$ 
D)  $x ^ { 15 }$ 
A)  $x ^ { 11 }$ 
B)  $x ^ { - 1 }$ 
C)  $x ^ { 10 }$ 
D)  $x ^ { 15 }$

Question 16

Factor the expression completely. $8 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 5$

Accepted Answer

A)  $( x - 1 ) \left( 8 x ^ { 2 } + 5 \right)$ 
B)  $\quad ( 1 - x ) \left( 8 x ^ { 2 } - 5 \right)$ 
C)  $( x + 1 ) \left( 8 x ^ { 2 } - 5 \right)$ 
D)  $\quad ( x + 1 ) \left( 5 - 8 x ^ { 2 } \right)$ 
A)  $( x - 1 ) \left( 8 x ^ { 2 } + 5 \right)$ 
B)  $\quad ( 1 - x ) \left( 8 x ^ { 2 } - 5 \right)$ 
C)  $( x + 1 ) \left( 8 x ^ { 2 } - 5 \right)$ 
D)  $\quad ( x + 1 ) \left( 5 - 8 x ^ { 2 } \right)$

Question 17

Give the degree of the polynomial. $\sqrt { 791 }$

Accepted Answer

A)  $1 / 2$ 
B)  0 
C)  This is not a polynomial 
D)  No defined degree 
A)  $1 / 2$ 
B)  0 
C)  This is not a polynomial 
D)  No defined degree

Question 18

Simplify the expression. $$\left( \frac { a ^ { - 1 } } { b ^ { - 4 } } \right) ^ { - 5 }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $\quad \frac { a ^ { 20 } } { b ^ { 5 } }$ 
B)  $\quad \frac { b ^ { 5 } } { a ^ { 20 } }$ 
C)  $\quad \frac { a ^ { 5 } } { b ^ { 20 } }$ 
D)  $\frac { b ^ { 20 } } { a ^ { 5 } }$ 
A)  $\quad \frac { a ^ { 20 } } { b ^ { 5 } }$ 
B)  $\quad \frac { b ^ { 5 } } { a ^ { 20 } }$ 
C)  $\quad \frac { a ^ { 5 } } { b ^ { 20 } }$ 
D)  $\frac { b ^ { 20 } } { a ^ { 5 } }$

Question 19

Factor the expression completely. $10 x ^ { 2 } + 5 x ^ { 3 }$

Accepted Answer

A)  $\quad 5 x ^ { 2 } ( 2 - x )$ 
B)  $\quad 5 x ^ { 2 } \left( 2 + x ^ { 2 } \right)$ 
C)  $\quad 5 x ^ { 2 } ( 3 + x )$ 
D)  $\quad 5 x ^ { 2 } ( 2 + x )$ 
A)  $\quad 5 x ^ { 2 } ( 2 - x )$ 
B)  $\quad 5 x ^ { 2 } \left( 2 + x ^ { 2 } \right)$ 
C)  $\quad 5 x ^ { 2 } ( 3 + x )$ 
D)  $\quad 5 x ^ { 2 } ( 2 + x )$

Question 20

Perform the operations and simplify. $$\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }$$
Assume that no denominators are 0 .

Accepted Answer

A)  $\quad \frac { 2 x - 36 } { x ^ { 2 } - 36 }$ 
B)  $\quad \frac { 2 x - 36 } { x ^ { 2 } - 6 }$ 
C)  $\quad \frac { 2 x + 6 } { x ^ { 2 } - 36 }$ 
D)  $\frac { 2 x - 6 } { x ^ { 2 } - 36 }$ 
A)  $\quad \frac { 2 x - 36 } { x ^ { 2 } - 36 }$ 
B)  $\quad \frac { 2 x - 36 } { x ^ { 2 } - 6 }$ 
C)  $\quad \frac { 2 x + 6 } { x ^ { 2 } - 36 }$ 
D)  $\frac { 2 x - 6 } { x ^ { 2 } - 36 }$

Simplify the expression. $\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }$

Give the degree of the polynomial. $\sqrt { 576 }$

Give the degree of the polynomial. $\sqrt { 127 }$

Simplify the expression. $( - 4 x ) ^ { 0 }$ Write the answer without using exponents.

Express the number -187,000,000 in scientific notation.

Simplify the expression. $\left( - \frac { 343 x ^ { 9 } } { 125 y ^ { 3 } } \right) ^ { 1 / 3 }$

Identify the correct union of intervals for the inequality. $x \leq - 18$ or $x > 4$

Perform the operation and simplify. $( a - 8 ) ^ { 2 }$

Simplify the expression. $( - 13 x ) ^ { 0 }$ Write the answer without using exponents.

Simplify the expression. $- 8 ^ { 4 / 3 }$

Simplify the expression. $\left( \frac { 8 x ^ { - 4 } y ^ { 5 } z ^ { - 8 } } { 32 x ^ { 4 } y ^ { 12 } z ^ { - 13 } } \right) ^ { 3 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Simplify the expression. $\left( x ^ { 3 } \right) ^ { 3 } \left( x ^ { 3 } \right) ^ { 2 }$

Factor the expression completely. $8 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 5$

Give the degree of the polynomial. $\sqrt { 791 }$

Simplify the expression. $\left( \frac { a ^ { - 1 } } { b ^ { - 4 } } \right) ^ { - 5 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Factor the expression completely. $10 x ^ { 2 } + 5 x ^ { 3 }$

Perform the operations and simplify. $\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }$ Assume that no denominators are 0 .

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 1: A Review of Basic Algebra

Simplify the expression. (625y4)1/4\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }(625y4)1/4

Give the degree of the polynomial. 576\sqrt { 576 }576​

Give the degree of the polynomial. 127\sqrt { 127 }127​

Simplify the expression. (−4x)0( - 4 x ) ^ { 0 }(−4x)0 Write the answer without using exponents.

Express the number -187,000,000 in scientific notation.

Simplify the expression. (−343x9125y3)1/3\left( - \frac { 343 x ^ { 9 } } { 125 y ^ { 3 } } \right) ^ { 1 / 3 }(−125y3343x9​)1/3

Identify the correct union of intervals for the inequality. x≤−18x \leq - 18x≤−18 or x>4x > 4x>4

Perform the operation and simplify. (a−8)2( a - 8 ) ^ { 2 }(a−8)2

Simplify the expression. (−13x)0( - 13 x ) ^ { 0 }(−13x)0 Write the answer without using exponents.

Simplify the expression. −84/3- 8 ^ { 4 / 3 }−84/3

Simplify the expression. (x3)3(x3)2\left( x ^ { 3 } \right) ^ { 3 } \left( x ^ { 3 } \right) ^ { 2 }(x3)3(x3)2

Factor the expression completely. 8x3+8x2−5x−58 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 58x3+8x2−5x−5

Give the degree of the polynomial. 791\sqrt { 791 }791​

Simplify the expression. (a−1b−4)−5\left( \frac { a ^ { - 1 } } { b ^ { - 4 } } \right) ^ { - 5 }(b−4a−1​)−5 Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Factor the expression completely. 10x2+5x310 x ^ { 2 } + 5 x ^ { 3 }10x2+5x3

Perform the operations and simplify. x+3x2+9x+18+xx2−36\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }x2+9x+18x+3​+x2−36x​ Assume that no denominators are 0 .

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Simplify the expression. $\left( 625 y ^ { 4 } \right) ^ { 1 / 4 }$

Give the degree of the polynomial. $\sqrt { 576 }$

Give the degree of the polynomial. $\sqrt { 127 }$

Simplify the expression. $( - 4 x ) ^ { 0 }$ Write the answer without using exponents.

Simplify the expression. $\left( - \frac { 343 x ^ { 9 } } { 125 y ^ { 3 } } \right) ^ { 1 / 3 }$

Identify the correct union of intervals for the inequality. $x \leq - 18$ or $x > 4$

Perform the operation and simplify. $( a - 8 ) ^ { 2 }$

Simplify the expression. $( - 13 x ) ^ { 0 }$ Write the answer without using exponents.

Simplify the expression. $- 8 ^ { 4 / 3 }$

Simplify the expression. $\left( x ^ { 3 } \right) ^ { 3 } \left( x ^ { 3 } \right) ^ { 2 }$

Factor the expression completely. $8 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 5$

Give the degree of the polynomial. $\sqrt { 791 }$

Simplify the expression. $\left( \frac { a ^ { - 1 } } { b ^ { - 4 } } \right) ^ { - 5 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Factor the expression completely. $10 x ^ { 2 } + 5 x ^ { 3 }$

Perform the operations and simplify. $\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }$ Assume that no denominators are 0 .