Question 1

Simplify the following expression. Do not use parentheses or negative exponents in your answer. $$\frac { x ^ { 14 } x ^ { - 5 } } { x ^ { 4 } x ^ { 2 } }$$

Accepted Answer

A)  $x ^ { 4 }$ 
B)  $x ^ { 3 }$ 
C)  $x ^ { - 4 }$ 
D)  $x ^ { - 3 }$ 
E)  $x ^ { 5 }$ 
A)  $x ^ { 4 }$ 
B)  $x ^ { 3 }$ 
C)  $x ^ { - 4 }$ 
D)  $x ^ { - 3 }$ 
E)  $x ^ { 5 }$

Question 2

In the expression -92, what is the base?

Accepted Answer

Question 3

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in scientific notation. $\frac { 3,600,000,000 } { 0.00006 }$

Accepted Answer

A) 6 13 
B) (6)(10) 13 
C) 6 -13 
D) (6)(10) -13 
E) (6)(10) 11 
A) 6 13 
B) (6)(10) 13 
C) 6 -13 
D) (6)(10) -13 
E) (6)(10) 11

Question 4

Simplify the expression. $( 19 x - 11 y ) - ( 3 x + 9 y )$

Accepted Answer

A)  $22 x - 2 y$ 
B)  $16 x - 2 y$ 
C)  $16 x - 20 y$ 
D)  $22 x - 20 y$ 
E) none of these 
A)  $22 x - 2 y$ 
B)  $16 x - 2 y$ 
C)  $16 x - 20 y$ 
D)  $22 x - 20 y$ 
E) none of these

Question 5

Simplify the following expression. $$x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$$

Accepted Answer

A)  $x ^ { 6 }$ 
B)  $x ^ { 8 }$ 
C)  $6 x ^ { 16 }$ 
D)  $x ^ { 16 }$ 
E)  $x ^ { 18 }$ 
A)  $x ^ { 6 }$ 
B)  $x ^ { 8 }$ 
C)  $6 x ^ { 16 }$ 
D)  $x ^ { 16 }$ 
E)  $x ^ { 18 }$

Question 6

Perform the division. If there is a remainder, leave the answer in $\text { quotient } + \frac { \text { remainder } } { \text { divisor } }$ form. $\frac { 3 x ^ { 2 } - 17 x + 11 } { 3 x - 2 }$

Accepted Answer

A)  $x - 7 + \frac { 1 } { 3 x - 2 }$ 
B)  $x - 5 + \frac { x - 5 } { 3 x - 2 }$ 
C)  $x - 5 + \frac { 1 } { 3 x - 2 }$ 
D)  $x - 5 + \frac { 6 } { 3 x - 2 }$ 
E)  $x + 7 + \frac { 6 } { 3 x - 2 }$ 
A)  $x - 7 + \frac { 1 } { 3 x - 2 }$ 
B)  $x - 5 + \frac { x - 5 } { 3 x - 2 }$ 
C)  $x - 5 + \frac { 1 } { 3 x - 2 }$ 
D)  $x - 5 + \frac { 6 } { 3 x - 2 }$ 
E)  $x + 7 + \frac { 6 } { 3 x - 2 }$

Question 7

Write the number $( 1.13 ) ( 10 ) ^ { - 1 }$ in ordinary decimal notation. For example, (2.78)(10) 4 = 27,800.

Accepted Answer

A) 0.113 
B) 0.0113 
C) 0.00113 
D) 113 
E) 1,130 
A) 0.113 
B) 0.0113 
C) 0.00113 
D) 113 
E) 1,130

Question 8

Write the number $( 5.5 ) ( 10 ) ^ { 7 }$ in ordinary decimal notation. For example, (2.78)(10) 4 = 27,800.

Accepted Answer

A) 550 
B) 55,000,000 
C) 5,500,000 
D) 5,500,000,000 
E) .0000000550 
A) 550 
B) 55,000,000 
C) 5,500,000 
D) 5,500,000,000 
E) .0000000550

Question 9

$- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }$

Accepted Answer

A) True 
 B)False

Question 10

Divide. $\frac { 4 y ^ { 3 } + 34 } { y + 4 }$

Accepted Answer

A)  $4 y ^ { 2 } - 16 y + 64 + \frac { - 222 } { ( y + 4 ) }$ 
B)  $4 y ^ { 2 } - 16 y - 64 + \frac { 222 } { ( y + 4 ) }$ 
C)  $4 y ^ { 2 } + 16 y + 64 + \frac { 222 } { ( y + 4 ) }$ 
D)  $- 4 y ^ { 2 } + 16 y + 64 + \frac { 222 } { ( y + 4 ) }$ 
E) none of these 
A)  $4 y ^ { 2 } - 16 y + 64 + \frac { - 222 } { ( y + 4 ) }$ 
B)  $4 y ^ { 2 } - 16 y - 64 + \frac { 222 } { ( y + 4 ) }$ 
C)  $4 y ^ { 2 } + 16 y + 64 + \frac { 222 } { ( y + 4 ) }$ 
D)  $- 4 y ^ { 2 } + 16 y + 64 + \frac { 222 } { ( y + 4 ) }$ 
E) none of these

Question 11

Find the product. $$( 4 a - 4 t ) ^ { 2 }$$

Accepted Answer

A)  $16 a ^ { 2 } - 4 a - 4 t + 16 t ^ { 2 }$ 
B)  $16 a ^ { 2 } - 16 t ^ { 2 }$ 
C)  $16 a ^ { 2 } + 16 t ^ { 2 }$ 
D)  $16 a ^ { 2 } - 32 a t + 16 t ^ { 2 }$ 
E)  $16 a ^ { 2 } - 16 a t + 16 t ^ { 2 }$ 
A)  $16 a ^ { 2 } - 4 a - 4 t + 16 t ^ { 2 }$ 
B)  $16 a ^ { 2 } - 16 t ^ { 2 }$ 
C)  $16 a ^ { 2 } + 16 t ^ { 2 }$ 
D)  $16 a ^ { 2 } - 32 a t + 16 t ^ { 2 }$ 
E)  $16 a ^ { 2 } - 16 a t + 16 t ^ { 2 }$

Question 12

Write the expression without using exponents. $19.3 c ^ { 0 }$

Accepted Answer

A) 1 
B) 19.3 
C) -19.3 
D) 0 
A) 1 
B) 19.3 
C) -19.3 
D) 0

Question 13

Select the expression that completes the formula below. $$( x y ) ^ { k }$$

Accepted Answer

A)  $x ^ { k } y ^ { k }$ 
B)  $x ^ { m + k }$ 
C)  $x ^ { m k }$ 
D)  $\frac { x ^ { k } } { y ^ { k } }$ 
E) None of these 
A)  $x ^ { k } y ^ { k }$ 
B)  $x ^ { m + k }$ 
C)  $x ^ { m k }$ 
D)  $\frac { x ^ { k } } { y ^ { k } }$ 
E) None of these

Question 14

Simplify the expression. $$\left( 2 y ^ { 2 } \right) ^ { 4 }$$

Accepted Answer

A)  $16 y ^ { 6 }$ 
B)  $16 y ^ { 8 }$ 
C)  $2 y ^ { 8 }$ 
D)  $16 y ^ { 4 }$ 
E)  $2 y ^ { 2 }$ 
A)  $16 y ^ { 6 }$ 
B)  $16 y ^ { 8 }$ 
C)  $2 y ^ { 8 }$ 
D)  $16 y ^ { 4 }$ 
E)  $2 y ^ { 2 }$

Question 15

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. $\frac { ( 480,000 ) ( 0.036 ) } { ( 0.0009 ) ( 600 ) }$

Accepted Answer

A) 3,200 
B) 32 
C) 115,200,000 
D) 32,000 
E) 11,520,000,000 
A) 3,200 
B) 32 
C) 115,200,000 
D) 32,000 
E) 11,520,000,000

Question 16

Divide $x ^ { 2 } - 6 x + 8$ by $x - 2$ .

Accepted Answer

A)  $x - 4$ 
B)  $x ^ { 2 } - 4 x + 10$ 
C)  $x ^ { 2 } - 4$ 
D)  $x + 4$ 
E)  $x - 6$ 
A)  $x - 4$ 
B)  $x ^ { 2 } - 4 x + 10$ 
C)  $x ^ { 2 } - 4$ 
D)  $x + 4$ 
E)  $x - 6$

Question 17

Simplify the following expression. $$d ^ { ( 8 n + 8 ) } d ^ { ( - 5 n ) }$$

Accepted Answer

A)  $d ^ { ( - 3 n + 8 ) }$ 
B)  $d ^ { - ( 3 n + 8 ) }$ 
C)  $d ^ { ( - ( 8 n + 8 ) 5 n ) }$ 
D)  $d ^ { ( 11 n ) }$ 
E)  $d ^ { ( 3 n + 8 ) }$ 
A)  $d ^ { ( - 3 n + 8 ) }$ 
B)  $d ^ { - ( 3 n + 8 ) }$ 
C)  $d ^ { ( - ( 8 n + 8 ) 5 n ) }$ 
D)  $d ^ { ( 11 n ) }$ 
E)  $d ^ { ( 3 n + 8 ) }$

Question 18

Find the product. $( 8 z + 1 ) ( 8 z - 1 )$

Accepted Answer

A)  $64 z ^ { 2 } - 1$ 
B)  $64 z ^ { 2 } - 16 z - 1$ 
C)  $64 z ^ { 2 } + 1$ 
D)  $16 z ^ { 2 } - 1$ 
E)  $16 z ^ { 2 } + 1$ 
A)  $64 z ^ { 2 } - 1$ 
B)  $64 z ^ { 2 } - 16 z - 1$ 
C)  $64 z ^ { 2 } + 1$ 
D)  $16 z ^ { 2 } - 1$ 
E)  $16 z ^ { 2 } + 1$

Question 19

Combine the like terms. 7 y and 6 y

Accepted Answer

A) 13 y 
B) 15 y 
C) 12 y 
D) 13 
E) 42 y 
A) 13 y 
B) 15 y 
C) 12 y 
D) 13 
E) 42 y

Question 20

Simplify the following expression. $$\frac { 1 } { 2 ^ { - 2 } }$$

Accepted Answer

A)  $- 4$ 
B)  $\frac { 1 } { 4 }$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $4$ 
E) 1 
A)  $- 4$ 
B)  $\frac { 1 } { 4 }$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $4$ 
E) 1

Simplify the following expression. Do not use parentheses or negative exponents in your answer. $\frac { x ^ { 14 } x ^ { - 5 } } { x ^ { 4 } x ^ { 2 } }$

In the expression -9², what is the base?

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in scientific notation. $\frac { 3,600,000,000 } { 0.00006 }$

Simplify the expression. $( 19 x - 11 y ) - ( 3 x + 9 y )$

Simplify the following expression. $x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$

Perform the division. If there is a remainder, leave the answer in $\text { quotient } + \frac { \text { remainder } } { \text { divisor } }$ form. $\frac { 3 x ^ { 2 } - 17 x + 11 } { 3 x - 2 }$

Write the number $( 1.13 ) ( 10 ) ^ { - 1 }$ in ordinary decimal notation. For example, (2.78)(10) ⁴ = 27,800.

Write the number $( 5.5 ) ( 10 ) ^ { 7 }$ in ordinary decimal notation. For example, (2.78)(10) ⁴ = 27,800.

$- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }$

Divide. $\frac { 4 y ^ { 3 } + 34 } { y + 4 }$

Find the product. $( 4 a - 4 t ) ^ { 2 }$

Write the expression without using exponents. $19.3 c ^ { 0 }$

Select the expression that completes the formula below. $( x y ) ^ { k }$

Simplify the expression. $\left( 2 y ^ { 2 } \right) ^ { 4 }$

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. $\frac { ( 480,000 ) ( 0.036 ) } { ( 0.0009 ) ( 600 ) }$

Divide $x ^ { 2 } - 6 x + 8$ by $x - 2$ .

Simplify the following expression. $d ^ { ( 8 n + 8 ) } d ^ { ( - 5 n ) }$

Find the product. $( 8 z + 1 ) ( 8 z - 1 )$

Combine the like terms. 7 y and 6 y

Simplify the following expression. $\frac { 1 } { 2 ^ { - 2 } }$

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 5: Exponents and Polynomials

Simplify the following expression. Do not use parentheses or negative exponents in your answer. x14x−5x4x2\frac { x ^ { 14 } x ^ { - 5 } } { x ^ { 4 } x ^ { 2 } }x4x2x14x−5​

In the expression -92, what is the base?

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in scientific notation. 3,600,000,0000.00006\frac { 3,600,000,000 } { 0.00006 }0.000063,600,000,000​

Simplify the expression. (19x−11y)−(3x+9y)( 19 x - 11 y ) - ( 3 x + 9 y )(19x−11y)−(3x+9y)

Simplify the following expression. x4⋅x2(x4⋅x2)(x4⋅x2)x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)x4⋅x2(x4⋅x2)(x4⋅x2)

Perform the division. If there is a remainder, leave the answer in quotient + remainder divisor \text { quotient } + \frac { \text { remainder } } { \text { divisor } } quotient + divisor remainder ​ form. 3x2−17x+113x−2\frac { 3 x ^ { 2 } - 17 x + 11 } { 3 x - 2 }3x−23x2−17x+11​

Write the number (1.13)(10)−1( 1.13 ) ( 10 ) ^ { - 1 }(1.13)(10)−1 in ordinary decimal notation. For example, (2.78)(10) 4 = 27,800.

Write the number (5.5)(10)7( 5.5 ) ( 10 ) ^ { 7 }(5.5)(10)7 in ordinary decimal notation. For example, (2.78)(10) 4 = 27,800.

−8t(−8t)=(−8t)2- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }−8t(−8t)=(−8t)2

Divide. 4y3+34y+4\frac { 4 y ^ { 3 } + 34 } { y + 4 }y+44y3+34​

Find the product. (4a−4t)2( 4 a - 4 t ) ^ { 2 }(4a−4t)2

Write the expression without using exponents. 19.3c019.3 c ^ { 0 }19.3c0

Select the expression that completes the formula below. (xy)k( x y ) ^ { k }(xy)k

Simplify the expression. (2y2)4\left( 2 y ^ { 2 } \right) ^ { 4 }(2y2)4

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (480,000)(0.036)(0.0009)(600)\frac { ( 480,000 ) ( 0.036 ) } { ( 0.0009 ) ( 600 ) }(0.0009)(600)(480,000)(0.036)​

Divide x2−6x+8x ^ { 2 } - 6 x + 8x2−6x+8 by x−2x - 2x−2 .

Simplify the following expression. d(8n+8)d(−5n)d ^ { ( 8 n + 8 ) } d ^ { ( - 5 n ) }d(8n+8)d(−5n)

Find the product. (8z+1)(8z−1)( 8 z + 1 ) ( 8 z - 1 )(8z+1)(8z−1)

Combine the like terms. 7 y and 6 y

Simplify the following expression. 12−2\frac { 1 } { 2 ^ { - 2 } }2−21​

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Simplify the following expression. Do not use parentheses or negative exponents in your answer. $\frac { x ^ { 14 } x ^ { - 5 } } { x ^ { 4 } x ^ { 2 } }$

In the expression -9², what is the base?

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in scientific notation. $\frac { 3,600,000,000 } { 0.00006 }$

Simplify the expression. $( 19 x - 11 y ) - ( 3 x + 9 y )$

Simplify the following expression. $x ^ { 4 } \cdot x ^ { 2 } \left( x ^ { 4 } \cdot x ^ { 2 } \right) \left( x ^ { 4 } \cdot x ^ { 2 } \right)$

Perform the division. If there is a remainder, leave the answer in $\text { quotient } + \frac { \text { remainder } } { \text { divisor } }$ form. $\frac { 3 x ^ { 2 } - 17 x + 11 } { 3 x - 2 }$

Write the number $( 1.13 ) ( 10 ) ^ { - 1 }$ in ordinary decimal notation. For example, (2.78)(10) ⁴ = 27,800.

Write the number $( 5.5 ) ( 10 ) ^ { 7 }$ in ordinary decimal notation. For example, (2.78)(10) ⁴ = 27,800.

$- 8 t ( - 8 t ) = ( - 8 t ) ^ { 2 }$

Divide. $\frac { 4 y ^ { 3 } + 34 } { y + 4 }$

Find the product. $( 4 a - 4 t ) ^ { 2 }$

Write the expression without using exponents. $19.3 c ^ { 0 }$

Select the expression that completes the formula below. $( x y ) ^ { k }$

Simplify the expression. $\left( 2 y ^ { 2 } \right) ^ { 4 }$

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. $\frac { ( 480,000 ) ( 0.036 ) } { ( 0.0009 ) ( 600 ) }$

Divide $x ^ { 2 } - 6 x + 8$ by $x - 2$ .

Simplify the following expression. $d ^ { ( 8 n + 8 ) } d ^ { ( - 5 n ) }$

Find the product. $( 8 z + 1 ) ( 8 z - 1 )$

Simplify the following expression. $\frac { 1 } { 2 ^ { - 2 } }$