Deck 12: Exponents and Polynomials

Question 1

Use the product rule to simplify. Write the results using exponents.

- $x ^ { 5 } \cdot x ^ { 11 }$

A) $x ^ { 55 }$
B) $x ^ { 16 }$
C) $2 x ^ { 55 }$
D) $2 x ^ { 16 }$

Answer 1

$x ^ { 16 }$

Question 2

Evaluate the expression.

- $- 91$

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

Answer 2

-9

Question 3

Evaluate the expression.

-- $- 44$

A)256
B)-16
C)-256
D)16

Answer 3

-256

Question 4

Evaluate the expression with the given replacement values.

- $x ^ { 2 }$ when x = -8

A)16
B)64
C)-64
D)-16

Question 5

Evaluate the expression.

- $7 \cdot 2 ^ { 3 }$

A)42
B)56
C)2744
D)15

Question 6

Evaluate the expression with the given replacement values.

- $\frac { 2 } { 9 x ^ { 2 } }$ when x = -6

A) $- \frac { 1 } { 162 }$
B) $- \frac { 1 } { 54 }$
C) $\frac { 1 } { 162 }$
D) $\frac { 1 } { 54 }$

Question 7

Use the product rule to simplify. Write the results using exponents.

- $x \cdot x ^ { 12 }$

A) $x ^ { 12 }$
B) $2 x ^ { 12 }$
C) $2 x ^ { 13 }$
D) $x ^ { 13 }$

Question 8

Evaluate the expression.

- $5 ^ { 4 }$

A)-20
B)625
C)20
D)-625

Question 9

Use the product rule to simplify. Write the results using exponents.

-( $( 5 x ) \left( 3 x ^ { 4 } \right) \left( x ^ { 3 } \right)$

A) $9 x ^ { 8 }$
B) $15 x ^ { 7 }$
C) $15 x ^ { 8 }$
D) $8 x ^ { 7 }$

Question 10

Evaluate the expression.

- $( - 4 ) ^ { 3 }$

A)64
B)-64
C)12
D)-12

Question 11

Evaluate the expression with the given replacement values.

- $x ^ { 5 }$ when x = -2

A)32
B)10
C)-10
D)-32

Question 12

Use the product rule to simplify. Write the results using exponents.

- $( - 3 ) ^ { 9 } \cdot ( - 3 ) ^ { 8 }$

A) $3 ^ { 17 }$
B) $( - 3 ) ^ { 17 }$
C) $917$
D)- $- 972$

Question 13

Evaluate the expression with the given replacement values.

- $6 x ^ { 2 }$ when x = 7

A)252
B)84
C)294
D)1764

Question 14

Use the product rule to simplify. Write the results using exponents.

- $x ^ { 9 } \cdot x ^ { 3 } \cdot x ^ { 5 }$

A) $x _ { x } ^ { 17 }$
B) $x ^ { 8 }$
C) $x ^ { 12 }$
D) $x ^ { 32 }$

Question 15

Evaluate the expression with the given replacement values.

-- $- 2 x ^ { 3 } y$ y w hen x = 2 and y = -3

A)36
B)48
C)24
D)-48

Question 16

Use the product rule to simplify. Write the results using exponents.

- $\left( - 9 x ^ { 3 } y \right) \left( - 9 x ^ { 5 } y ^ { 2 } \right)$

A)- $- 81 x ^ { 8 } y ^ { 2 }$
B) $81 x ^ { 15 } y ^ { 2 }$
C) $- 81 x ^ { 8 } y ^ { 3 }$
D)81 $81 x ^ { 8 } y ^ { 3 }$

Question 17

Use the product rule to simplify. Write the results using exponents.

- $\left( 9 p ^ { 3 } \right) \left( 7 p ^ { 9 } \right)$

A) $63 p ^ { 27 }$
B) $63 p ^ { 12 }$
C)- $- 63 p ^ { 12 }$
D)- $- 63 p ^ { 27 }$

Question 18

Use the product rule to simplify. Write the results using exponents.

- $( - 7 ) ^ { 9 } \cdot ( - 7 ) ^ { 7 }$

A) $- 716$
B) $4963$
C) $( - 7 ) ^ { 16 }$
D) $4916$

Question 19

Evaluate the expression.

- $\left( \frac { 1 } { 8 } \right) ^ { 2 }$

A) $\frac { 1 } { 10 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 16 }$
D) $\frac { 1 } { 64 }$

Question 20

Use the product rule to simplify. Write the results using exponents.

- $25 \cdot 23$

A) $4 ^ { 15 }$
B) $215$
C) $4 ^ { 8 }$
D) $2 ^ { 8 }$

Question 21

Use the product rule to simplify. Write the results using exponents.

-The rectangle below has widthidth $7 x ^ { 4 }$ feet and feet and lengthlength $4 x ^ { 6 }$ feet. Find the area as an expression of x.

A) $11 x ^ { 10 } s q f t$
B) $28 x ^ { 11 } \mathrm { sq } \mathrm { ft }$
C) $11 x ^ { 11 } s q f t$
D) $28 x ^ { 10 } \mathrm { sq } \mathrm { ft }$

Question 22

Use the power rule to simplify.

- $\left( 5 ^ { 6 } \right) ^ { 10 }$

A) $5 ^ { 16 }$
B) $25 ^ { 6 }$
C) $25^{60}$
D) $5 ^ { 60 }$

Question 23

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( \frac { x } { y } \right) ^ { 5 }$

A) $x ^ { 5 } y ^ { 5 }$
B) $\frac { x ^ { 5 } } { y ^ { 5 } }$
C) $\frac { x ^ { 5 } } { y }$
D) $\frac { y ^ { 5 } } { x ^ { 5 } }$

Question 24

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( - 6 x ^ { 3 } y ^ { 6 } z \right) ^ { 2 }$

A) $12 x ^ { 6 } y ^ { 12 } z ^ { 2 }$
B) $36 x ^ { 6 } y ^ { 12 } z ^ { 2 }$
C) $- 6 x ^ { 5 } y ^ { 8 } z$
D) $- 36 x ^ { 6 } y ^ { 12 } z ^ { 2 }$

Question 25

Use the quotient rule to simplify the expression.

- $\frac { ( - 4 ) ^ { 19 } } { ( - 4 ) ^ { 17 } }$

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

Question 26

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $( 3 a ) ^ { 4 }$

A) $12 a ^ { 4 }$
B)81a
C) $81 a ^ { 4 }$
D)12a

Question 27

Use the power rule to simplify.

- $\left( - 7 ^ { 4 } \right) ^ { 6 }$

A) $( - 49 ) ^ { 4 }$
B) $( - 7 ) ^ { 10 }$
C) $( - 49 ) ^ { 24 }$
D) $( - 7 ) ^ { 24 }$

Question 28

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( \frac { 2 p ^ { 4 } v ^ { 2 } } { s ^ { 3 } } \right) ^ { 2 }$

A) $\frac { 4 p ^ { 8 } v ^ { 4 } } { s ^ { 6 } }$
B) $\frac { 2 p ^ { 8 } v ^ { 4 } } { s ^ { 6 } }$
C) $\frac { 2 p ^ { 8 } v ^ { 4 } } { s ^ { 5 } }$
D) $\frac { 4 p ^ { 6 } v ^ { 4 } } { s ^ { 5 } }$

Question 29

Use the quotient rule to simplify the expression.

- $\frac { x ^ { 5 } } { x ^ { 4 } }$

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

Question 30

Use the power rule to simplify.

- $\left( x ^ { 5 } \right) ^ { 7 }$

A) $x ^ { 12 }$
B) $x ^ { 35 }$
C) $7 x ^ { 35 }$
D) $7 x ^ { 5 }$

Question 31

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( \frac { - 3 x y ^ { 8 } } { z ^ { 4 } } \right) ^ { 3 }$

A)- $- \frac { 27 x ^ { 3 } y ^ { 8 } } { z ^ { 4 } }$
B)- $- \frac { 9 x y ^ { 24 } } { z ^ { 12 } }$
C) $\frac { 27 x ^ { 3 } y ^ { 24 } } { z ^ { 4 } }$
D) $- \frac { 27 x ^ { 3 } y ^ { 24 } } { z ^ { 12 } }$

Question 32

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( - 7 x ^ { 4 } y ^ { 6 } z \right) ^ { 3 }$

A) $- 343 x ^ { 12 } y ^ { 18 } z ^ { 3 }$
B)- $- 343 x ^ { 4 } y ^ { 6 } z$
C) $- 21 x ^ { 13 } y ^ { 19 } z ^ { 4 }$
D) $343 x ^ { 7 } y ^ { 9 } z$

Question 33

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $( - 2 a ) ^ { 6 }$

A) $64 a ^ { 6 }$
B)64a
C)-12a
D) $- 12 a 6$

Question 34

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $( - 3 x y ) ^ { 4 }$

A)-12xy
B)81xy
C) $81 x ^ { 4 } y ^ { 4 }$
D) $- 12 x ^ { 4 } y ^ { 4 }$

Question 35

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( x ^ { 9 } y \right) ^ { 3 }$

A) $x ^ { 27 } y ^ { 3 }$
B) $x ^ { 12 } y$
C) $x ^ { 27 } y$
D) $x ^ { 12 } y ^ { 4 }$

Question 36

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( \frac { x y ^ { 5 } } { - 3 z ^ { 7 } } \right) ^ { 2 }$

A) $\frac { x ^ { 2 } y ^ { 10 } } { 9 z ^ { 14 } }$
B) $- \frac { x y ^ { 10 } } { 9 z ^ { 14 } }$
C) $\frac { x ^ { 2 } y ^ { 7 } } { 9 z ^ { 9 } }$
D) $\frac { x y ^ { 10 } } { 3 z ^ { 14 } }$

Question 37

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( \frac { a b } { 8 c } \right) ^ { 3 }$

A) $\frac { a b ^ { 3 } } { 8 c ^ { 3 } }$
B) $\frac { a ^ { 3 } b ^ { 3 } } { 8 \mathrm { c } }$
C) $\frac { a ^ { 4 } b ^ { 4 } } { 4096 c ^ { 4 } }$
D) $\frac { a ^ { 3 } b ^ { 3 } } { 512 c ^ { 3 } }$

Question 38

Use the quotient rule to simplify the expression.

- $\frac { f ^ { 9 } } { f }$

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

Question 39

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $\left( \frac { \mathrm { pm } ^ { 7 } } { \mathrm { q } ^ { 3 } } \right) ^ { 3 }$

A) $\frac { p ^ { 3 } m ^ { 10 } } { q ^ { 6 } }$
B) $\frac { \mathrm { p } ^ { 3 } \mathrm {~m} ^ { 21 } } { \mathrm { q } ^ { 9 } }$
C) $\frac { \mathrm { pm } 10 } { \mathrm { q } ^ { 6 } }$
D) $\frac { \mathrm { pm } ^ { 21 } } { \mathrm { q } ^ { 9 } }$

Question 40

Use the power rule and the power of a product or quotient rule to simplify the expression.

- $( - 4 \mathrm { pqr } ) ^ { 2 }$

A)-8pqr
B)16pqr
C)- $- 8 p ^ { 2 } q ^ { 2 } r ^ { 2 }$
D) $16 p ^ { 2 } q ^ { 2 } r ^ { 2 }$

Question 41

Simplify the expression.

- $\frac { 2 x ^ { 7 } } { x ^ { 4 } }$

A)6x
B) $2 x ^ { 11 }$
C) $8 x ^ { 3 }$
D) $2 x ^ { 3 }$

Question 42

Simplify the expression.

- $- 3 y ^ { 0 }$

A)-2
B)-3
C)1
D)0

Question 43

Simplify the expression.

- $\left( - 4 x ^ { 6 } y \right) \left( 6 x ^ { 6 } y ^ { 3 } \right)$

A) $24 x ^ { 12 } y ^ { 2 }$
B) $24 x ^ { 36 } y ^ { 3 }$
C) $- 24 x ^ { 12 } y ^ { 4 }$
D)-24x36y3

Question 44

Simplify the expression.

- $- 5 ^ { 2 }$

A)10
B)-25
C)25
D)-10

Question 45

Simplify the expression.

- $( 6 a b ) ^ { 2 }$

A) $6 a ^ { 2 } b ^ { 2 }$
B) $8 a ^ { 2 } b ^ { 2 }$
C) $36 a ^ { 2 } b ^ { 2 }$
D) $12 a ^ { 2 } b ^ { 2 }$

Question 46

Simplify the expression.

- $( - 2 x ) ^ { 0 }$

A)-1
B)1
C)-2
D)0

Question 47

Simplify the expression.

- $\left( - 2 z ^ { 2 } \right) \left( 3 z ^ { 3 } \right)$

A) $108 z ^ { 5 }$
B)- $- 6 z ^ { 6 }$
C) $6 z ^ { 6 }$
D)- $- 6 z ^ { 5 }$

Question 48

Use the quotient rule to simplify the expression.

- $\frac { 42 m ^ { 5 } n ^ { 7 } } { 6 m ^ { 4 } n ^ { 2 } }$

A) $42 m n ^ { 5 }$
B) $7 m ^ { 9 } n ^ { 9 }$
C) $7 n ^ { 5 }$
D) $7 \mathrm { mn } ^ { 5 }$

Question 49

Simplify the expression.

- $120 + 110$

A)0
B)1
C)23
D)2

Question 50

Simplify the expression.

- $\frac { x ^ { 10 } y ^ { 16 } } { x ^ { 4 } y ^ { 8 } }$

A) $x ^ { 6 } y ^ { 8 }$
B) $x ^ { 10 } y ^ { 16 }$
C) $x ^ { 6 } + y ^ { 8 }$
D) $- x ^ { 6 } y ^ { 8 }$

Question 51

Use the quotient rule to simplify the expression.

- $\frac { s ^ { 14 } t ^ { 7 } } { s ^ { 2 } t }$

A) $\mathrm { s } ^ { 12 \mathrm { t } ^ { 5 } }$
B) $s ^ { 12 } t ^ { 7 }$
C) $s _ { s } ^ { 12 } t ^ { 6 }$
D) $\mathrm { s } ^ { 16 } \mathrm { t } ^ { 8 }$

Question 52

Simplify the expression.

- $- 4 x ^ { 0 }$

A)-4
B)-3
C)-4x + 1
D)-8

Question 53

Simplify the expression.

- $y ^ { 5 } y ^ { y }$

A) $y ^ { 6 }$
B) $y ^ { 5 }$
C) $2 y ^ { 5 }$
D) $2 y ^ { 6 }$

Question 54

Simplify the expression.

- $z ^ { 0 } + 2 ^ { 0 }$

A)z + 2
B)2
C)3
D)0

Question 55

Simplify the expression.

- $g ^ { 6 } g ^ { 5 } g ^ { 5 }$

A) $\mathrm { g } ^ { 16 }$
B) $g ^ { 35 }$
C) $\mathrm { g } ^ { 11 }$
D) $\mathrm { g } ^ { 10 }$

Question 56

Simplify the expression.

- $\left( - 7 x ^ { 7 } y z ^ { 8 } \right) ^ { 3 }$

A)- $- 21 x ^ { 21 } y _ { z } 24$
B) $343 x ^ { 21 } y ^ { 3 } z ^ { 24 }$
C) $21 x ^ { 21 } y z ^ { 24 }$
D)- $- 343 x ^ { 21 } y ^ { 3 } z ^ { 24 }$

Question 57

Simplify the expression.

- $( 14 b ) ^ { 0 }$

A)14
B)0
C)1
D)b

Question 58

Simplify the expression.

- $\left( - 4 x ^ { 5 } y z ^ { 7 } \right) ^ { 2 }$

A) $16 x ^ { 10 } y ^ { 2 } z ^ { 14 }$
B) $8 x ^ { 10 } y _ { y } 14$
C)- $- 8 x ^ { 10 } y z ^ { 14 }$
D)- $- 16 x ^ { 10 } y ^ { 2 } z ^ { 14 }$

Question 59

Simplify the expression.

- $( - 9 ) ^ { 0 } + ( - 5 ) ^ { 0 }$

A)0
B)-14
C)2
D)-2

Question 60

Simplify the expression.

- $\mathrm { y } ^ { 11 } \mathrm { y } ^ { 12 }$

A) $2 y ^ { 23 }$
B) $y ^ { 23 }$
C) $y ^ { 132 }$ 132
D) $2 y ^ { 132 }$ 132

Question 61

Simplify the expression. Write the result using positive exponents only.

- $\left( \frac { 1 } { 2 } \right) ^ { - 3 }$

A)8
B) $\frac { 1 } { 6 }$
C) $\frac { 1 } { 8 }$
D)-8

Question 62

Simplify the expression. Write the result using positive exponents only.

- $\mathrm { r } ^ { - 7 }$

A) $\frac { 1 } { \mathrm { r } ^ { 7 } }$
B)- $- \frac { 1 } { \mathrm { r } ^ { 7 } }$
C) $\mathrm { r } ^ { 1 / 7 }$
D) $- \mathbf { r } ^ { 7 }$

Question 63

Simplify the expression. Write the result using positive exponents only.

- $x ^ { - 5 } \cdot x ^ { 3 }$

A) $x ^ { 2 }$
B) $x ^ { 8 }$
C) $\frac { 1 } { x ^ { 8 } }$
D) $\frac { 1 } { x ^ { 2 } }$

Question 64

Simplify the expression. Write the result using positive exponents only.

- $- 5 ^ { - 3 }$

A)125
B)-125
C) $\frac { 1 } { 15 }$
D) $- \frac { 1 } { 125 }$

Question 65

Simplify the expression.

- $\frac { ( 30 \mathrm { pq } ) ^ { 3 } } { 125 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } }$

A) $\frac { 6 } { 25 }$
B) $\frac { 216 } { 25 p ^ { 2 } q ^ { 2 } }$
C) $216 p ^ { 6 } q ^ { 6 }$
D)216

Question 66

Simplify the expression. Write the result using positive exponents only.

- $m ^ { - 6 } \cdot m ^ { - 7 } \cdot m ^ { - 4 } \cdot m$

A) $m ^ { 16 }$
B) $m ^ { 168 }$
C) $\frac { 1 } { m ^ { 16 } }$
D) $\frac { 1 } { m ^ { 168 } }$

Question 67

Simplify the expression.

- $2 ^ { 2 } + 2 ^ { 3 }$

A)12
B)64
C)32
D)10

Question 68

Simplify the expression.

- $\frac { \left( x ^ { 2 } \right) ^ { 4 } } { ( 7 x ) ^ { 3 } }$

A) $\frac { x ^ { 5 } } { 7 }$
B) $\frac { x ^ { 11 } } { 343 }$
C) $\frac { x ^ { 3 } } { 343 }$
D) $\frac { x ^ { 5 } } { 343 }$

Question 69

Simplify the expression. Write the result using positive exponents only.

- $\frac { x ^ { 2 } } { x ^ { 5 } }$

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

Question 70

Simplify the expression. Write the result using positive exponents only.

- $\frac { 1 } { m ^ { - 5 } }$

A) $- m ^ { 1 / 5 }$
B) $\mathrm { m } ^ { 1 / 5 }$
C) $\mathrm { m } ^ { 5 }$
D) $- m ^ { 5 }$

Question 71

Simplify the expression. Write the result using positive exponents only.

- $2 ^ { - 3 }$

A) $\frac { 1 } { 6 }$
B)-8
C)8
D) $\frac { 1 } { 8 }$

Question 72

Simplify the expression.

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

A) $\frac { 243 x ^ { 15 } } { y ^ { 10 } }$
B) $\frac { 244 x ^ { 8 } } { y ^ { 7 } }$
C) $\frac { 243 x } { y ^ { 2 } }$
D) $\frac { 3 x ^ { 15 } } { y ^ { 10 } }$

Question 73

Simplify the expression. Write the result using positive exponents only.

- $\frac { y ^ { - 9 } } { y ^ { 2 } }$

A) $\frac { 1 } { y ^ { 7 } }$
B) $\frac { 1 } { y ^ { 11 } }$
C) $y ^ { 11 }$
D) $\frac { 1 } { y ^ { 18 } }$

Question 74

Simplify the expression.

- $\frac { 3 a ^ { 12 } b ^ { 3 } c ^ { 4 } } { a b c }$

A) $\frac { 3 a ^ { 11 } b ^ { 2 } c ^ { 3 } } { a b c }$
B) $3 a ^ { 13 } b ^ { 4 } c ^ { 5 }$
C) $\frac { a ^ { 11 } b ^ { 2 } c ^ { 3 } } { 3 }$
D) $3 a ^ { 11 } b ^ { 2 } c ^ { 3 }$

Question 75

Simplify the expression. Write the result using positive exponents only.

- $\frac { p ^ { 6 } } { p ^ { - 8 } }$

A) $p ^ { 48 }$
B) $p ^ { 14 }$
C) $\frac { 1 } { \mathrm { p } ^ { 14 } }$
D) $\frac { 1 } { p ^ { 48 } }$

Question 76

Simplify the expression. Write the result using positive exponents only.

- $- 6 z ^ { - 4 }$

A) $\frac { 1296 } { z ^ { 4 } }$
B)- $- \frac { 6 } { z ^ { 4 } }$
C) $\frac { 1 } { 1296 z ^ { 4 } }$
D) $- \frac { 1 } { 1296 z ^ { 4 } }$

Question 77

Simplify the expression. Write the result using positive exponents only.

- $3 ^ { - 1 } + 4 ^ { - 1 }$

A) $\frac { 7 } { 12 }$
B)- 1
C) $\frac { 12 } { 7 }$
D)2

Question 78

Simplify the expression. Write the result using positive exponents only.

- $( - 5 ) ^ { - 2 }$

A)25
B)-25
C) $\frac { 1 } { 25 }$
D) $- \frac { 1 } { 25 }$

Question 79

Simplify the expression. Write the result using positive exponents only.

- $\frac { x ^ { - 5 } } { x ^ { - 9 } }$

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

Question 80

Simplify the expression.

- $\left( \frac { 12 t ^ { 3 } } { 6 s ^ { 4 } } \right) ^ { 2 }$

A) $\frac { 4 t ^ { 6 } } { s ^ { 4 } }$
B) $\frac { 2 t ^ { 6 } } { s ^ { 8 } }$
C) $\frac { 4 t ^ { 6 } } { s ^ { 8 } }$
D) $\frac { 4 t ^ { 5 } } { s ^ { 6 } }$