Question 1

Rationalize the numerator and simplify. $\frac { \sqrt { 5 } } { 20 }$

Accepted Answer

A)  $\quad \frac { 1 } { 4 \sqrt { 3 } }$ 
B)  $\quad \frac { 1 } { 4 \sqrt { 5 } }$ 
C)  $\quad \frac { 1 } { 8 \sqrt { 3 } }$ 
D)  $\frac { 1 } { 4 \sqrt { 9 } }$ 
E)  $\frac { 1 } { 5 \sqrt { 5 } }$ 
A)  $\quad \frac { 1 } { 4 \sqrt { 3 } }$ 
B)  $\quad \frac { 1 } { 4 \sqrt { 5 } }$ 
C)  $\quad \frac { 1 } { 8 \sqrt { 3 } }$ 
D)  $\frac { 1 } { 4 \sqrt { 9 } }$ 
E)  $\frac { 1 } { 5 \sqrt { 5 } }$

Question 2

Factor the expression completely. $64 x ^ { 10 } + 1$

Accepted Answer

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

Question 3

Simplify the expression. $$\frac { 1 } { x ^ { - 8 } }$$
Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $\frac { 1 } { x ^ { 9 } }$ 
B)  $x ^ { 8 }$ 
C)  $x ^ { 9 }$ 
D)  $\frac { 1 } { x ^ { 8 } }$ 
A)  $\frac { 1 } { x ^ { 9 } }$ 
B)  $x ^ { 8 }$ 
C)  $x ^ { 9 }$ 
D)  $\frac { 1 } { x ^ { 8 } }$

Question 4

Factor the expression completely. $64 x ^ { 10 } + 1$

Accepted Answer

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

Question 5

Perform the multiplication and simplify. $$( x - y ) ( 4 x + 14 y ) ^ { 2 }$$

Accepted Answer

A)  $\quad 16 x ^ { 3 } + 84 x ^ { 2 } y + 196 x y ^ { 2 } + 96 y ^ { 3 }$ 
B)  $\quad 16 x ^ { 3 } + 96 x ^ { 2 } y + 84 x y ^ { 2 } + 196 y ^ { 3 }$ 
C)  $\quad 16 x ^ { 3 } + 96 x ^ { 2 } y + 84 x y ^ { 2 } - 196 y ^ { 3 }$ 
D)  $\quad 196 x ^ { 3 } + 84 x ^ { 2 } y + 96 x y ^ { 2 } + 16 y ^ { 3 }$ 
E)  $\quad 16 x ^ { 3 } - 96 x ^ { 2 } y + 84 x y ^ { 2 } + 196 y ^ { 3 }$ 
A)  $\quad 16 x ^ { 3 } + 84 x ^ { 2 } y + 196 x y ^ { 2 } + 96 y ^ { 3 }$ 
B)  $\quad 16 x ^ { 3 } + 96 x ^ { 2 } y + 84 x y ^ { 2 } + 196 y ^ { 3 }$ 
C)  $\quad 16 x ^ { 3 } + 96 x ^ { 2 } y + 84 x y ^ { 2 } - 196 y ^ { 3 }$ 
D)  $\quad 196 x ^ { 3 } + 84 x ^ { 2 } y + 96 x y ^ { 2 } + 16 y ^ { 3 }$ 
E)  $\quad 16 x ^ { 3 } - 96 x ^ { 2 } y + 84 x y ^ { 2 } + 196 y ^ { 3 }$

Question 6

Simplify the expression. $- 16 ^ { 3 / 2 }$

Accepted Answer

A)  $- 192$ 
B)  67 
C)  $- 64$ 
D)  $- 66$ 
E) $-128$
F) $- 24$ 
A)  $- 192$ 
B)  67 
C)  $- 64$ 
D)  $- 66$ 
E) $-128$
F) $- 24$

Question 7

Simplify the expression. $\frac { 1 } { x ^ { - 7 } }$ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $x ^ { 7 }$ 
B)  $\frac { 1 } { x ^ { 8 } }$ 
C)  $x ^ { 8 }$ 
D)  $\frac { 1 } { x ^ { 7 } }$ 
A)  $x ^ { 7 }$ 
B)  $\frac { 1 } { x ^ { 8 } }$ 
C)  $x ^ { 8 }$ 
D)  $\frac { 1 } { x ^ { 7 } }$

Question 8

Simplify the complex fraction. $\frac { \frac { 3 x ^ { 5 } } { y ^ { 2 } } } { \frac { 6 x ^ { 2 } z ^ { 4 } } { y ^ { 4 } } }$ Assume that the denominators are not 0 .

Accepted Answer

A)  $ \frac { 1 } { 2 } x ^ { 3 } y ^ { 2 } z ^ { - 4 }$ 
B)  $\frac { 1 } { 2 } x ^ { 4 } y ^ { 2 } z ^ { 4 }$ 
C)  $ \frac { 1 } { 2 } x ^ { 5 } y ^ { 2 } z ^ { - 4 }$ 
D)  $\frac { 1 } { 2 } x ^ { 3 } y ^ { 2 } z ^ { - 4 }$ 
A)  $ \frac { 1 } { 2 } x ^ { 3 } y ^ { 2 } z ^ { - 4 }$ 
B)  $\frac { 1 } { 2 } x ^ { 4 } y ^ { 2 } z ^ { 4 }$ 
C)  $ \frac { 1 } { 2 } x ^ { 5 } y ^ { 2 } z ^ { - 4 }$ 
D)  $\frac { 1 } { 2 } x ^ { 3 } y ^ { 2 } z ^ { - 4 }$

Question 9

Rationalize the numerator and simplify. $\frac { \sqrt { 2 } } { 8 }$

Accepted Answer

A)  $\quad \frac { 1 } { 8 \sqrt { 5 } }$ 
B)  $\frac { 1 } { 4 \sqrt { 2 } }$ 
C)  $\frac { 1 } { 4 \sqrt { 6 } }$ 
D)  $\quad \frac { 1 } { 5 \sqrt { 2 } }$ 
E)  $\frac { 1 } { 4 \sqrt { 5 } }$ 
A)  $\quad \frac { 1 } { 8 \sqrt { 5 } }$ 
B)  $\frac { 1 } { 4 \sqrt { 2 } }$ 
C)  $\frac { 1 } { 4 \sqrt { 6 } }$ 
D)  $\quad \frac { 1 } { 5 \sqrt { 2 } }$ 
E)  $\frac { 1 } { 4 \sqrt { 5 } }$

Question 10

Write the expression without using absolute value symbols. $| x + 4 | - | x - 11 | \quad$ for $\quad x < - 8$
$| x + 4 | - | x - 11 | =ــــــــــــ$ for $x < - 8$

Accepted Answer

A)  15 
B)  $2 x - 15$ 
C)  7 
D)  $15 - 2 x$ 
E)  $- 15$ 
A)  15 
B)  $2 x - 15$ 
C)  7 
D)  $15 - 2 x$ 
E)  $- 15$

Question 11

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.
$$\sqrt { 4 } \sqrt [ 3 ] { 4 }$$

Accepted Answer

A)  $\sqrt { 1024 }$ 
B)  $\sqrt [ 6 ] { 1024 }$ 
C)  $\sqrt [ 3 ] { 1024 }$ 
D)  $\sqrt [ 6 ] { 4 }$ 
E)  $\sqrt [ 6 ] { 256 }$ 
A)  $\sqrt { 1024 }$ 
B)  $\sqrt [ 6 ] { 1024 }$ 
C)  $\sqrt [ 3 ] { 1024 }$ 
D)  $\sqrt [ 6 ] { 4 }$ 
E)  $\sqrt [ 6 ] { 256 }$

Question 12

Factor the expression completely. $25 x ^ { 8 } + 1$

Accepted Answer

A)  The expression is prime. 
B)  $\quad \left( 5 x ^ { 4 } + 1 \right) ^ { 2 }$ 
C)  $\quad \left( 5 x ^ { 4 } - 1 \right) ^ { 2 }$ 
D)  $\quad \left( 5 x ^ { 4 } + 1 \right) \left( 5 x ^ { 4 } - 1 \right)$ 
A)  The expression is prime. 
B)  $\quad \left( 5 x ^ { 4 } + 1 \right) ^ { 2 }$ 
C)  $\quad \left( 5 x ^ { 4 } - 1 \right) ^ { 2 }$ 
D)  $\quad \left( 5 x ^ { 4 } + 1 \right) \left( 5 x ^ { 4 } - 1 \right)$

Question 13

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. $\frac { \sqrt [ 4 ] { 2 } } { \sqrt { 6 } }$

Accepted Answer

A) $\frac { \sqrt [ 4 ] { 72 } } { 6 }$ 
B)  $\frac { \sqrt [ 5 ] { 72 } } { 6 }$ 
C)  $\frac { \sqrt [ 4 ] { 72 } } { 8 }$ 
D)  $\frac { \sqrt [ 4 ] { 72 } } { 2 }$ 
A) $\frac { \sqrt [ 4 ] { 72 } } { 6 }$ 
B)  $\frac { \sqrt [ 5 ] { 72 } } { 6 }$ 
C)  $\frac { \sqrt [ 4 ] { 72 } } { 8 }$ 
D)  $\frac { \sqrt [ 4 ] { 72 } } { 2 }$

Question 14

Perform the operations and simplify. $$\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }$$
Assume that no denominators are 0 .

Accepted Answer

A)  $\frac { 2 x - 49 } { x ^ { 2 } - 7 }$ 
B)  $\frac { 2 x - 7 } { x ^ { 2 } - 49 }$ 
C)  $\frac { 2 x - 7 } { x ^ { 2 } + 49 }$ 
D)  $\frac { 2 x + 7 } { x ^ { 2 } - 49 }$ 
A)  $\frac { 2 x - 49 } { x ^ { 2 } - 7 }$ 
B)  $\frac { 2 x - 7 } { x ^ { 2 } - 49 }$ 
C)  $\frac { 2 x - 7 } { x ^ { 2 } + 49 }$ 
D)  $\frac { 2 x + 7 } { x ^ { 2 } - 49 }$

Question 15

Simplify the expression. $\left( \frac { 5 x ^ { - 5 } y ^ { 5 } z ^ { - 7 } } { 20 x ^ { 6 } y ^ { 10 } z ^ { - 12 } } \right) ^ { 3 }$ 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) $\frac { z ^ { 5 } } { 4 x ^ { 33 } y ^ { 15 } }$ 
B) 
$\frac { z ^ { 15 } } { 64 x ^ { 33 } y ^ { 15 } }$ 
C)  $\quad \frac { z ^ { 15 } } { 64 x ^ { 15 } y ^ { 33 } }$ 
D) $\frac { z ^ { 5 } } { 4 x ^ { 11 } y ^ { 5 } }$ 
E) $\frac { z ^ { 15 } } { 64 x ^ { - 33 } y ^ { - 15 } }$ 
A) $\frac { z ^ { 5 } } { 4 x ^ { 33 } y ^ { 15 } }$ 
B) 
$\frac { z ^ { 15 } } { 64 x ^ { 33 } y ^ { 15 } }$ 
C)  $\quad \frac { z ^ { 15 } } { 64 x ^ { 15 } y ^ { 33 } }$ 
D) $\frac { z ^ { 5 } } { 4 x ^ { 11 } y ^ { 5 } }$ 
E) $\frac { z ^ { 15 } } { 64 x ^ { - 33 } y ^ { - 15 } }$

Question 16

Calculate the volume of a box that has dimensions of 6,000 by 8,600 by 4,800 millimeters.

Accepted Answer

A)  $\quad 2.4768 \times 10 ^ { 10 } \mathrm {~mm} ^ { 3 }$ 
B)  $\quad 2.4768 \times 10 ^ { 11 } \mathrm {~mm} ^ { 3 }$ 
C)  $\quad 1.9975 \times 10 ^ { 10 } \mathrm {~mm} ^ { 3 }$ 
D)  $\quad 1.9975 \times 10 ^ { 11 } \mathrm {~mm} ^ { 3 }$ 
A)  $\quad 2.4768 \times 10 ^ { 10 } \mathrm {~mm} ^ { 3 }$ 
B)  $\quad 2.4768 \times 10 ^ { 11 } \mathrm {~mm} ^ { 3 }$ 
C)  $\quad 1.9975 \times 10 ^ { 10 } \mathrm {~mm} ^ { 3 }$ 
D)  $\quad 1.9975 \times 10 ^ { 11 } \mathrm {~mm} ^ { 3 }$

Question 17

Factor the expression completely. $$( 4 x - 5 y ) ^ { 3 } + 64$$

Accepted Answer

A)  $( 4 x - 5 y + 4 ) \cdot \left( 16 x ^ { 2 } + 16 x + 40 x y - 20 y - 25 y ^ { 2 } + 16 \right)$ 
B)  $( 4 x - 5 y + 4 ) \cdot \left( 16 x ^ { 2 } - 16 x + 40 x y - 20 y + 25 y ^ { 2 } + 16 \right)$ 
C)  $( 4 x + 5 y - 4 ) \cdot \left( 16 x ^ { 2 } + 16 x + 40 x y - 20 y - 25 y ^ { 2 } + 16 \right)$ 
D)  $( 4 x + 5 y - 4 ) \cdot \left( 16 x ^ { 2 } - 16 x - 40 x y + 20 y + 25 y ^ { 2 } + 16 \right)$ 
E)  $( 4 x - 5 y + 4 ) \cdot \left( 16 x ^ { 2 } - 16 x - 40 x y + 20 y + 25 y ^ { 2 } + 16 \right)$ 
A)  $( 4 x - 5 y + 4 ) \cdot \left( 16 x ^ { 2 } + 16 x + 40 x y - 20 y - 25 y ^ { 2 } + 16 \right)$ 
B)  $( 4 x - 5 y + 4 ) \cdot \left( 16 x ^ { 2 } - 16 x + 40 x y - 20 y + 25 y ^ { 2 } + 16 \right)$ 
C)  $( 4 x + 5 y - 4 ) \cdot \left( 16 x ^ { 2 } + 16 x + 40 x y - 20 y - 25 y ^ { 2 } + 16 \right)$ 
D)  $( 4 x + 5 y - 4 ) \cdot \left( 16 x ^ { 2 } - 16 x - 40 x y + 20 y + 25 y ^ { 2 } + 16 \right)$ 
E)  $( 4 x - 5 y + 4 ) \cdot \left( 16 x ^ { 2 } - 16 x - 40 x y + 20 y + 25 y ^ { 2 } + 16 \right)$

Question 18

Factor the expression completely. $8 r ^ { 2 } - 16 r s - 90 s ^ { 2 }$

Accepted Answer

A)  $\quad ( 2 r + 9 s ) ( 4 r - 10 s )$ 
B)  $\quad ( 9 r - 2 s ) ( 4 r + 10 s )$ 
C)  $( 2 r - 9 s ) ( 4 r + 10 s )$ 
D)  $\quad ( 2 r - 9 s ) ( 10 r + 4 s )$ 
A)  $\quad ( 2 r + 9 s ) ( 4 r - 10 s )$ 
B)  $\quad ( 9 r - 2 s ) ( 4 r + 10 s )$ 
C)  $( 2 r - 9 s ) ( 4 r + 10 s )$ 
D)  $\quad ( 2 r - 9 s ) ( 10 r + 4 s )$

Question 19

Express the number -176,000,000 in scientific notation.

Accepted Answer

A)  $ - 1.76 \times 10 ^ { 8 }$ 
B)  $- 1.76 \times 10 ^ { 7 }$ 
C)  $- 17.6 \times 10 ^ { 9 }$ 
D)  $\quad - 1.76 \times 10 ^ { 9 }$ 
A)  $ - 1.76 \times 10 ^ { 8 }$ 
B)  $- 1.76 \times 10 ^ { 7 }$ 
C)  $- 17.6 \times 10 ^ { 9 }$ 
D)  $\quad - 1.76 \times 10 ^ { 9 }$

Question 20

Factor the expression completely. $4 r ^ { 2 } - 4 r s - 35 s ^ { 2 }$

Accepted Answer

A)  $\quad ( 7 r - 2 s ) ( 2 r + 5 s )$ 
B)  $\quad ( 2 r - 7 s ) ( 2 r + 5 s )$ 
C)  $\quad ( 2 r + 7 s ) ( 2 r - 5 s )$ 
D)  $\quad ( 2 r - 7 s ) ( 5 r + 2 s )$ 
A)  $\quad ( 7 r - 2 s ) ( 2 r + 5 s )$ 
B)  $\quad ( 2 r - 7 s ) ( 2 r + 5 s )$ 
C)  $\quad ( 2 r + 7 s ) ( 2 r - 5 s )$ 
D)  $\quad ( 2 r - 7 s ) ( 5 r + 2 s )$

Rationalize the numerator and simplify. $\frac { \sqrt { 5 } } { 20 }$

Factor the expression completely. $64 x ^ { 10 } + 1$

Simplify the expression. $\frac { 1 } { x ^ { - 8 } }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Factor the expression completely. $64 x ^ { 10 } + 1$

Perform the multiplication and simplify. $( x - y ) ( 4 x + 14 y ) ^ { 2 }$

Simplify the expression. $- 16 ^ { 3 / 2 }$

Simplify the expression. $\frac { 1 } { x ^ { - 7 } }$ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Simplify the complex fraction. $\frac { \frac { 3 x ^ { 5 } } { y ^ { 2 } } } { \frac { 6 x ^ { 2 } z ^ { 4 } } { y ^ { 4 } } }$ Assume that the denominators are not 0 .

Rationalize the numerator and simplify. $\frac { \sqrt { 2 } } { 8 }$

Write the expression without using absolute value symbols. $| x + 4 | - | x - 11 | \quad$ for $\quad x < - 8$ $| x + 4 | - | x - 11 | =ــــــــــــ$ for $x < - 8$

Factor the expression completely. $25 x ^ { 8 } + 1$

Perform the operations and simplify. $\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }$ Assume that no denominators are 0 .

Simplify the expression. $\left( \frac { 5 x ^ { - 5 } y ^ { 5 } z ^ { - 7 } } { 20 x ^ { 6 } y ^ { 10 } z ^ { - 12 } } \right) ^ { 3 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Calculate the volume of a box that has dimensions of 6,000 by 8,600 by 4,800 millimeters.

Factor the expression completely. $( 4 x - 5 y ) ^ { 3 } + 64$

Factor the expression completely. $8 r ^ { 2 } - 16 r s - 90 s ^ { 2 }$

Express the number -176,000,000 in scientific notation.

Factor the expression completely. $4 r ^ { 2 } - 4 r s - 35 s ^ { 2 }$

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

Rationalize the numerator and simplify. 520\frac { \sqrt { 5 } } { 20 }205​​

Factor the expression completely. 64x10+164 x ^ { 10 } + 164x10+1

Simplify the expression. 1x−8\frac { 1 } { x ^ { - 8 } }x−81​ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Factor the expression completely. 64x10+164 x ^ { 10 } + 164x10+1

Perform the multiplication and simplify. (x−y)(4x+14y)2( x - y ) ( 4 x + 14 y ) ^ { 2 }(x−y)(4x+14y)2

Simplify the expression. −163/2- 16 ^ { 3 / 2 }−163/2

Simplify the expression. 1x−7\frac { 1 } { x ^ { - 7 } }x−71​ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Simplify the complex fraction. 3x5y26x2z4y4\frac { \frac { 3 x ^ { 5 } } { y ^ { 2 } } } { \frac { 6 x ^ { 2 } z ^ { 4 } } { y ^ { 4 } } }y46x2z4​y23x5​​ Assume that the denominators are not 0 .

Rationalize the numerator and simplify. 28\frac { \sqrt { 2 } } { 8 }82​​

Factor the expression completely. 25x8+125 x ^ { 8 } + 125x8+1

Perform the operations and simplify. x+6x2+13x+42+xx2−49\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }x2+13x+42x+6​+x2−49x​ Assume that no denominators are 0 .

Calculate the volume of a box that has dimensions of 6,000 by 8,600 by 4,800 millimeters.

Factor the expression completely. (4x−5y)3+64( 4 x - 5 y ) ^ { 3 } + 64(4x−5y)3+64

Factor the expression completely. 8r2−16rs−90s28 r ^ { 2 } - 16 r s - 90 s ^ { 2 }8r2−16rs−90s2

Express the number -176,000,000 in scientific notation.

Factor the expression completely. 4r2−4rs−35s24 r ^ { 2 } - 4 r s - 35 s ^ { 2 }4r2−4rs−35s2

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

Rationalize the numerator and simplify. $\frac { \sqrt { 5 } } { 20 }$

Factor the expression completely. $64 x ^ { 10 } + 1$

Simplify the expression. $\frac { 1 } { x ^ { - 8 } }$ Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.

Factor the expression completely. $64 x ^ { 10 } + 1$

Perform the multiplication and simplify. $( x - y ) ( 4 x + 14 y ) ^ { 2 }$

Simplify the expression. $- 16 ^ { 3 / 2 }$

Simplify the expression. $\frac { 1 } { x ^ { - 7 } }$ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Simplify the complex fraction. $\frac { \frac { 3 x ^ { 5 } } { y ^ { 2 } } } { \frac { 6 x ^ { 2 } z ^ { 4 } } { y ^ { 4 } } }$ Assume that the denominators are not 0 .

Rationalize the numerator and simplify. $\frac { \sqrt { 2 } } { 8 }$

Factor the expression completely. $25 x ^ { 8 } + 1$

Perform the operations and simplify. $\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }$ Assume that no denominators are 0 .

Factor the expression completely. $( 4 x - 5 y ) ^ { 3 } + 64$

Factor the expression completely. $8 r ^ { 2 } - 16 r s - 90 s ^ { 2 }$

Factor the expression completely. $4 r ^ { 2 } - 4 r s - 35 s ^ { 2 }$