Deck 4: Polynomials: Operations

Question 1

What is the meaning of the expression?
$0.05 ^ { 3 }$

A) $0.000216$
B) $3 \cdot 0.05$
C) $0.00000625$
D) $0.05 \cdot 0.05 \cdot 0.05$

Answer 1

D

Question 2

Evaluate.
$( - 9 ) ^ { 0 }$

A) 1
B) 0
C) $- 1$
D) $- 9$

Answer 2

A

Question 3

Evaluate.
$6.74 ^ { 1 }$

A) 0
B) $6.74$
C) $45.43$
D) 1

Answer 3

B

Question 4

What is the meaning of the expression?
$17 ^ { 2 }$

A) 578
B) 19
C) $2 \cdot 17$
D) $17 \cdot 17$

Question 5

What is the meaning of the expression?
$- 3 q ^ { 3 }$

A) $( - 3 q ) ( - 3 q ) ( - 3 q )$
В) $( - 3 ) ( - 3 ) ( - 3 ) ( q )$
C) $- 3 \cdot \mathrm { q } \cdot \mathrm { q } \cdot \mathrm { q }$
D) $- 3 \cdot \mathrm { q } \cdot 3$

Question 6

Evaluate.
$\left( \frac { 4 } { 5 } \right) ^ { 1 }$

A) $\frac { 4 } { 5 }$
B) 1
C) $- \frac { 4 } { 5 }$
D) $\frac { 5 } { 4 }$

Question 7

Evaluate.
$\mathrm { cd } ^ { 0 }$

A) $c d$
B) $\mathrm { c }$
C) $\mathrm { d }$
D) 1

Question 8

Evaluate.
$b ^ { 1 }$

A) $b$
B) 1
C) $- 1$
D) 0

Question 9

What is the meaning of the expression?
$4 ^ { 2 }$

A) 6
B) $4 \cdot 4$
C) 3
D) $2 \cdot 4$

Question 10

What is the meaning of the expression?
$4 ^ { 6 }$

A) $4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$
B) $6 \cdot 4$
C) 5
D) 46

Question 11

Evaluate.
$( 4 x ) ^ { 0 ; } x \neq 0$

A) 4
B) $4 x$
C) 0
D) 1

Question 12

What is the meaning of the expression?
$\left( \frac { 4 } { 5 } \right) ^ { 4 }$

A) $4 \left( \frac { 4 } { 5 } \right)$
B) $\left( \frac { 4 } { 5 } \right) \left( \frac { 4 } { 5 } \right) \left( \frac { 4 } { 5 } \right) \left( \frac { 4 } { 5 } \right)$
C) $\frac { 4 \cdot 4 \cdot 4 \cdot 4 } { 5 }$
D) $\frac { 4 } { 5 \cdot 5 \cdot 5 \cdot 5 }$

Question 13

Evaluate.
$\left( - \frac { 3 } { 7 } \right) ^ { 0 }$

A) $\frac { 3 } { 7 }$
B) 1
C) 0
D) $- 1$

Question 14

Evaluate.
$12 ^ { 0 }$

A) 12
B) 1
C) 0
D) $- 1$

Question 15

Evaluate.
$xy^ { 1 }$

A) $y$
B) $x y$
C) $x$
D) 1

Question 16

Evaluate.
$- 12^0$

A) $- 12$
B) $- 1$
C) 0
D) 1

Question 17

What is the meaning of the expression?
$2 x ^ { 3 }$

A) $2 \cdot x \cdot x \cdot x$
B) $2 \cdot 2 \cdot 2 \cdot x$
C) $2 \mathrm { x } \cdot 2 \mathrm { x } \cdot 2 \mathrm { x }$
D) $2 \cdot x \cdot 3$

Question 18

What is the meaning of the expression?
$( - 3.7 ) ^ { 3 }$

A) $- 3.7 \cdot 3.7 \cdot 3.7$
B) $( 3.7 ) ( 3.7 ) ( 3.7 )$
C) $3 ( - 3.7 )$
D) $( - 3.7 ) ( - 3.7 ) ( - 3.7 )$

Question 19

Evaluate.
$m ^ { 4 }$ when $m = 3$

A) 5
B) 7
C) 81
D) 12

Question 20

Evaluate.
$$x ^ { 0 } ; x \neq 0$$

A) $- 1$
B) $x$
C) 1
D) 0

Question 21

Express the following using negative exponents.
$\frac { 1 } { 3 ^ { 9 } }$

A) $3 ^ { 9 }$
B) $3 ^ { - 9 }$
C) $9 ^ { - 3 }$
D) $3 - 10$

Question 22

Evaluate.
$- p ^ { 3 }$ , when $p = 7$

A) 4
B) 21
C) $- 343$
D) 343

Question 23

Evaluate.
$p ^ { 5 }$ , when $p = 0$

A) 1
B) 0
C) 5
D) 20

Question 24

Evaluate.
$x ^ { 2 } - 4$ when $x = - 7$

A) 33
B) 45
C) $- 11$
D) $x ^ { 2 } - 7$

Question 25

Express using positive exponents. Then simplify.
$$( - 4 ) ^ { - 2 }$$

A) $- \frac { 1 } { 16 }$
B) $\frac { 1 } { 16 }$
C) $- 16$
D) 16

Question 26

Express using positive exponents. Then simplify.
$$4 ^ { - 3 }$$

A) $\frac { 1 } { 12 }$
B) $- 64$
C) $\frac { 1 } { 64 }$
D) 64

Question 27

Evaluate.
The volume of a cylinder with height $\mathrm { h }$ and radius $\mathrm { r }$ is given by $\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h}$ . Find the volume of the cylinder. Use $3.14$ for $\pi$ .

A) $942 \mathrm {~m} ^ { 3 }$
B) $471 \mathrm {~m} ^ { 3 }$
C) $3532.5 \mathrm {~m} ^ { 3 }$
D) $14,130 \mathrm {~m} ^ { 3 }$

Question 28

Express using positive exponents. Then simplify.
$$\left( \frac { 1 } { 3 } \right) ^ { - 2 }$$

A) $\frac { 1 } { 6 }$
B) 9
C) $\frac { 1 } { 9 }$
D) $- 9$

Question 29

Express using positive exponents. Then simplify.
$x ^ { - 3 }$

A) $\frac { 1 } { x ^ { - 3 } }$
B) $x ^ { 3 }$
C) $\frac { 1 } { x ^ { 3 } }$
D) $3 \mathrm { x }$

Question 30

Evaluate.
The volume of a cube with sides of length s is given by $V = s ^ { 3 }$ . Find the volume of the cube.

A) 17,576 in. 3
B) 1352 in. 3
C) 78 in. 3
D) $676 \mathrm { in } ^ { 3 }$

Question 31

Express using positive exponents. Then simplify.
$\left( \frac { 1 } { 2 } \right) ^ { - 2 }$

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

Question 32

Express using positive exponents. Then simplify.
$\frac { 1 } { x ^ { - m } }$

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

Question 33

Evaluate.
$y ^ { 1 } - 6$ , when $y = - 9$

A) 45
В) $- 15$
C) 75
D) $- 6$

Question 34

Evaluate.
$y ^ { 16 }$ when $y = 1$

A) 16
B) 0
C) $- 1$
D) 1

Question 35

Express using positive exponents. Then simplify.
$\frac { 1 } { x ^ { - 8 } }$

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

Question 36

Express using positive exponents. Then simplify.
$- 3 ^ { - 2 }$

A) $\frac { 1 } { 6 }$
B) $- 9$
C) $- \frac { 1 } { 9 }$
D) 9

Question 37

Express the following using negative exponents.
$\frac { 1 } { 6 ^ { 3 } }$

A) $6 ^ { - 3 }$
B) $3 ^ { - 6 }$
C) $6 ^ { - 4 }$
D) $6 ^ { 3 }$

Question 38

Evaluate.
$\mathrm { m } ^ { 5 }$ when $\mathrm { m } = 2$

A) 25
B) 10
C) 4
D) 32

Question 39

Evaluate.
$\mathrm { m } ^ { 2 }$ when $\mathrm { m } = 19$

A) 21
B) 38
C) 361
D) 722

Question 40

Evaluate.
$x ^ { 1 }$ , when $x = 10$

A) 200
B) 20
C) 10
D) 12

Question 41

Divide and simplify.
$$\frac { p ^ { 4 } } { p ^ { - 4 } }$$

A) $\frac { 1 } { p ^ { 8 } }$
B) $\mathrm { p } ^ { 8 }$
C) $p ^ { - 8 }$
D) $\mathrm { p } ^ { 0 }$

Question 42

Multiply and simplify.
$y ^ { 20 } \cdot y ^ { 0 }$

A) $y ^ { 20 }$
B) 0
C) $y ^ { 200 }$
D) 1

Question 43

Divide and simplify.
$\frac { ( 29 x ) ^ { 7 } } { ( 29 x ) ^ { 8 } }$

A) $\frac { 1 } { 29 x ^ { 7 } }$
B) $29 x$
C) $\frac { 1 } { 29 x }$
D) $\frac { 1 } { x ^ { 7 } }$

Question 44

Multiply and simplify.
$$a ^ { - 6 } \cdot a ^ { 6 }$$

A) 0
B) $- 1$
C) 1
D) $\frac { 1 } { a ^ { 6 } }$

Question 45

Express the following using negative exponents.
$\frac { 1 } { \mathrm {~b} ^ { 3 } }$

A) $3 ^ { - b }$
B) $b ^ { - 3 }$
C) $3 ^ { - b - 1 }$
D) $b ^ { 3 }$

Question 46

Multiply and simplify.
$$\left( m n ^ { 4 } \right) \left( m ^ { 2 } n ^ { 5 } \right)$$

A) $m ^ { 2 } n ^ { 9 }$
B) $m ^ { 3 } n ^ { 9 }$
C) $2 m ^ { 3 } 2 n ^ { 9 }$
D) $m ^ { 2 } n ^ { 20 }$

Question 47

Multiply and simplify.
$$5 ^ { 11 } \cdot 5 ^ { - 3 }$$

A) $5 ^ { 11 }$
B) $5 ^ { 3 }$
C) $5 ^ { 5 }$
D) $5 ^ { 8 }$

Question 48

Multiply and simplify.
$$x \cdot x ^ { - 8 }$$

A) $\frac { 1 } { x ^ { 9 } }$
B) $x ^ { 9 }$
C) $\frac { 1 } { x ^ { 7 } }$
D) $x ^ { 7 }$

Question 49

Multiply and simplify.

- $3 ^ { 3 \cdot 3 ^ { 4 } }$

A) 7
B) 3 ¹¹
C) $3 ^ { 7 }$
D) 1

Question 50

Multiply and simplify.
$$y ^ { - 7 } \cdot y ^ { - 3 }$$

A) $\frac { 1 } { y ^ { 4 } }$
B) $\frac { 1 } { y ^ { - 10 } }$
C) $\frac { 1 } { \mathrm { y } ^ { 10 } }$
D) $\mathrm { y } ^ { 10 }$

Question 51

Express the following using negative exponents.
$\frac { 1 } { x ^ { 9 } }$

A) $x ^ { 9 }$
B) $9 ^ { - x }$
C) $9 ^ { - x + 1 }$
D) $x ^ { - 9 }$

Question 52

Express the following using negative exponents.
$\frac { 1 } { t ^ { 11 } }$

A) $11 ^ { \mathrm { t } }$
B) $11 ^ { - t }$
C) $\mathrm { t } ^ { 11 }$
D) $t ^ { - 11 }$

Question 53

Multiply and simplify.
$t ^ { 9 } \cdot t ^ { 3 }$

A) $t ^ { 6 }$
B) $\mathrm { t } ^ { 12 }$
C) $\frac { 1 } { t ^ { 12 } }$
D) $\frac { 1 } { t ^ { 6 } }$

Question 54

Multiply and simplify.
$\left( x ^ { 2 } y ^ { 6 } \right) \left( x ^ { 5 } y \right)$

A) $2 x ^ { 7 } 2 y ^ { 7 }$
B) $x ^ { 10 } y ^ { 6 }$
C) $x ^ { 7 } y ^ { 6 }$
D) $x ^ { 7 } y ^ { 7 }$

Question 55

Multiply and simplify.

- $$3 ^ { - 6 } \cdot 3 ^ { 8 }$$

A) 1
B) $3 ^ { 8 }$
C) $3 ^ { 10 }$
D) $3 ^ { 2 }$

Question 56

Divide and simplify.
$\frac { ( 4 p ) ^ { 10 } } { ( 4 p ) ^ { 7 } }$

A) $\frac { 1 } { 64 p ^ { 3 } }$
B) $64 p ^ { 3 }$
C) $\frac { p ^ { 3 } } { 64 }$
D) $\frac { 64 } { \mathrm { p } ^ { 3 } }$

Question 57

Multiply and simplify.
$\mathrm { x } ^ { - 9 } \cdot \mathrm { x } ^ { 3 } \cdot \mathrm { x } ^ { - 8 }$

A) $x ^ { 20 }$
B) $x ^ { 14 }$
C) $\frac { 1 } { x ^ { 20 } }$
D) $\frac { 1 } { \mathrm { x } ^ { 14 } }$

Question 58

Divide and simplify.
$\frac { t ^ { 5 } } { t ^ { 9 } }$

A) $t ^ { 4 }$
B) $\frac { t ^ { 5 } } { t ^ { 4 } }$
C) $t ^ { - 9 }$
D) $\frac { 1 } { t ^ { 4 } }$

Question 59

Divide and simplify.
$\frac { ( 11 x ) ^ { 16 } } { ( 11 x ) ^ { 16 } }$

A) $\frac { 1 } { x ^ { 16 } }$
B) $x ^ { 16 }$
C) 1
D) $x$

Question 60

Multiply and simplify.
(6x) ${ } ^ { 17 } ( 6 x ) ^ { 15 }$

A) $( 6 x ) ^ { 255 }$
B) $( 6 x ) ^ { 32 }$
C) $6 x ^ { 32 }$
D) $6 x ^ { 255 }$

Question 61

Divide and simplify.
$\frac { x } { x ^ { 12 } }$

A) $x ^ { 11 }$
B) $\frac { 1 } { \mathrm { x } ^ { 11 } }$
C) $x ^ { 12 }$
D) $\frac { 1 } { \mathrm { x } ^ { 12 } }$

Question 62

Simplify.
$- 5 \left( x ^ { - 5 } y ^ { - 1 } \right) ^ { - 4 }$

A) $\frac { - 5 } { x ^ { 20 } y ^ { 4 } }$
B) $( - 5 ) ^ { 4 } x ^ { 20 } y ^ { 4 }$
C) $\frac { x ^ { 20 } y ^ { 4 } } { ( - 5 ) ^ { 4 } }$
D) $- 5 x ^ { 20 } y ^ { 4 }$

Question 63

Simplify.
$\left( - 5 p ^ { 3 } q ^ { 3 } r ^ { 3 } \right) ^ { 5 }$

A) $( - 5 ) ^ { 5 } p ^ { 8 } q ^ { 8 } r ^ { 8 }$
B) $- 25 p ^ { 8 } q ^ { 8 } 8$
C) $( - 5 ) ^ { 5 } \mathrm { p } ^ { 15 } \mathrm { q } ^ { 15 } \mathrm { r } 15$
D) $( - 5 ) ^ { 15 } \mathrm { p } ^ { 15 } \mathrm { q } ^ { 15 } \mathrm { r } ^ { 15 }$

Question 64

Simplify.
$\left( \frac { x ^ { 7 } } { 3 } \right) ^ { 3 }$

A) $\frac { x ^ { 10 } } { 27 }$
B) $\frac { x ^ { 21 } } { 27 }$
C) $\frac { x ^ { 4 } } { 27 }$
D) $\frac { a ^ { 21 } } { 3 }$

Question 65

Simplify.
$$- 2 \left( x ^ { 3 } y \right) ^ { - 5 }$$

A) $- 2 x 15 y 5$
B) $\frac { 1 } { ( - 2 ) ^ { 5 } \mathrm { x } ^ { 15 } \mathrm { y } ^ { 5 } }$
C) $- 10 x ^ { 3 } y ^ { 5 }$
D) $\frac { - 2 } { x ^ { 15 } y ^ { 5 } }$

Question 66

Simplify.
$\left( - 3 a ^ { 4 } \right) ^ { 3 }$

A) $( - 3 ) ^ { 12 } a ^ { 4 }$
B) $- 9 a ^ { 4 }$
C) $( - 3 ) ^ { 3 } \mathrm { a } ^ { 12 }$
D) $( - 3 ) ^ { 12 } a ^ { 12 }$

Question 67

Simplify.
$\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { 2 }$

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

Question 68

Divide and simplify.
$\frac { t ^ { 8 } } { t }$

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

Question 69

Simplify.
$\left( 5 ^ { 5 } \right) ^ { - 4 }$

A) $5 ^ { 1 }$
B) $\frac { 1 } { 5 ^ { 20 } }$
C) $- 4 \cdot 5 ^ { 5 }$
D) $5 ^ { 20 }$

Question 70

Simplify.
$\left( \frac { 5 a } { 3 } \right) ^ { 2 }$

A) $\frac { 5 a ^ { 2 } } { 9 }$
B) $\frac { 25 a } { 9 }$
C) $\frac { 25 a ^ { 2 } } { 3 }$
D) $\frac { 25 a ^ { 2 } } { 9 }$

Question 71

Simplify.
$\left( \frac { 4 } { x } \right) ^ { 4 }$

A) $\frac { 256 } { x ^ { 4 } }$
B) $\frac { 256 } { \mathrm { x } }$
C) $256 x ^ { 4 }$
D) $\frac { 4 } { x ^ { 4 } }$

Question 72

Simplify.
$$\left( - 3 p ^ { - 2 } q ^ { 2 } r ^ { - 2 } \right) ^ { 6 }$$

A) $\frac { ( - 3 ) ^ { 6 } } { p ^ { 12 } q ^ { 12 } { } _ { r } 12 }$
B) $\frac { ( - 3 ) ^ { 6 } p ^ { 12 } } { q ^ { 12 } r ^ { 12 } }$
C) $\frac { ( - 3 ) ^ { 6 } q ^ { 12 } } { p ^ { 12 } r ^ { 12 } }$
D) $( - 3 ) ^ { 6 } \mathrm { p } ^ { 12 } \mathrm { q } ^ { 12 } { } _ { \mathrm { r } } ^ { 12 }$

Question 73

Divide and simplify.
$\frac { t ^ { - 3 } } { t ^ { - 7 } }$

A) $t ^ { - 4 }$
B) $t ^ { 4 }$
C) $\mathrm { t } ^ { 10 }$
D) $t ^ { - 10 }$

Question 74

Simplify.
$\left( \frac { x ^ { 4 } y } { z ^ { 2 } } \right) ^ { 3 }$

A) $\frac { x ^ { 12 } y ^ { 3 } } { z ^ { 2 } }$
B) $\frac { x ^ { 12 } y ^ { 3 } } { z ^ { 6 } }$
C) $\frac { x ^ { 7 } y ^ { 3 } } { z ^ { 5 } }$
D) $\frac { x ^ { 3 } y ^ { 12 } } { z ^ { 6 } }$

Question 75

Simplify.
$\left( \frac { 3 } { 4 y } \right) ^ { 3 }$

A) $\frac { 27 y ^ { 3 } } { 64 }$
B) $\frac { 27 } { 4 y ^ { 3 } }$
C) $\frac { 27 } { 64 y }$
D) $\frac { 27 } { 64 y ^ { 3 } }$

Question 76

Divide and simplify.
$\frac { z ^ { - 7 } } { z ^ { - 5 } }$

A) $\frac { 1 } { \mathrm { z } ^ { - 2 } }$
B) $z ^ { 2 }$
C) $\frac { 1 } { \mathrm { z } ^ { 2 } }$
D) $z ^ { 12 }$

Question 77

Simplify.
$$\left( \frac { 2 } { b ^ { - 4 } } \right) ^ { 6 }$$

A) $\frac { 64 } { \mathrm {~b} ^ { 24 } }$
B) $64 \mathrm {~b} ^ { 24 }$
C) $\frac { \mathrm { b } ^ { 24 } } { 64 }$
D) $\frac { 1 } { 64 b ^ { 24 } }$

Question 78

Divide and simplify.
$\frac { y ^ { - 13 } } { y ^ { 3 } }$

A) $\frac { 1 } { y ^ { - 10 } }$
B) $y ^ { 16 }$
C) $\mathrm { y } ^ { 10 }$
D) $\frac { 1 } { \mathrm { y } ^ { 16 } }$

Question 79

Simplify.
$\left( - 2 x ^ { 4 } y \right) ^ { 3 }$

A) $- 6 x ^ { 4 } y$
B) $- 6 x ^ { 4 } y ^ { 3 }$
C) $( - 2 ) ^ { 3 } x 12 y ^ { 3 }$
D) $( - 2 ) ^ { 3 } x ^ { 7 } y ^ { 3 }$

Question 80

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

A) $\frac { 1 } { x ^ { 6 } }$
B) $x ^ { 6 }$
C) $- 2 x ^ { - 3 }$
D) $x ^ { 1 }$