Deck 4: Polynomials: Operations

Question 1

What is the meaning of the expression?

-32

A) 3
B) $3 \cdot 3$
C) $2 \cdot 3$
D) 5

Answer 1

$3 \cdot 3$

Question 2

What is the meaning of the expression?

- $11^{2}$

A) $2 \cdot 11$
B) 13
C) 242
D) $11 \cdot 11$

Answer 2

$11 \cdot 11$

Question 3

What is the meaning of the expression?

- $3^{6}$

A) 5
B) $3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$
C) 36
D) $6 \cdot 3$

Answer 3

$3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Question 4

What is the meaning of the expression?

-0.073

A) 0.000512
B) $3 \cdot 0.07$
C) 0.00002401
D) $0.07 \cdot 0.07 \cdot 0.07$

Question 5

What is the meaning of the expression?

- $(-4.7)^{3}$

A) $-4.7 \cdot 4.7 \cdot 4.7$
B) $(4.7)(4.7)(4.7)$
C) $3(-4.7)$
D) $(-4.7)(-4.7)(-4.7)$

Question 6

What is the meaning of the expression?

- $\left(\frac{2}{5}\right)^{4}$

A) $\frac{2}{5 \cdot 5 \cdot 5 \cdot 5}$

B) $\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)$

C) $\frac{2 \cdot 2 \cdot 2 \cdot 2}{5}$

D) $4\left(\frac{2}{5}\right)$

Question 7

What is the meaning of the expression?

- $3 x^{3}$

A) $3 \cdot 3 \cdot 3 \cdot x$
B) $3 x \cdot 3 x \cdot 3 x$
C) $3 \cdot x \cdot 3$
D) $3 \cdot x \cdot x \cdot x$

Question 8

What is the meaning of the expression?

- $-4 q^{3}$

A) $(-4 q)(-4 q)(-4 q)$
B) $-4 \cdot q \cdot 3$
C) $-4 \cdot q \cdot q \cdot q$
D) $(-4)(-4)(-4)(q)$

Question 9

Evaluate.

- $15^{0}$

A) 15
B) 0
C) -1
D) 1

Question 10

Evaluate.

- $-3^{0}$

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

Question 11

Evaluate.

- $(-7)^{0}$

A) 1
B) 0
C) - 1
D) -7

Question 12

Evaluate.

- $x^{0} ; x \neq 0$

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

Question 13

Evaluate.

- $(6 \mathrm{x})^{0} ; \mathrm{x} \neq 0$

A) 0
B) 6
C) $6 x$
D) 1

Question 14

Evaluate.

- $a^{1}$

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

Question 15

Evaluate.

- $9^{1}$

A) 9
B) 81
C) 1
D) 0

Question 16

Evaluate.

- $\left(-\frac{2}{7}\right)^{0}$

A) 0
B) - 1
C) $\frac{2}{7}$
D) 1

Question 17

Evaluate.

- $\left(\frac{2}{5}\right)^{1}$

A) $\frac{2}{5}$
B) $\frac{5}{2}$
C) $-\frac{2}{5}$
D) 1

Question 18

Evaluate.

- $x y^{1}$

A) $x$
B) 1
C) $\mathrm{y}$
D) $x y$

Question 19

Evaluate.

- $\mathrm{cd}^{0}$

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

Question 20

Evaluate.

- $m^{3}$ when $m=5$

A) 125
B) 4
C) 15
D) 8

Question 21

Evaluate.

- $m^{2}$ when $m=10$

A) 20
B) 12
C) 200
D) 100

Question 22

Evaluate.

- $m^{4}$ when $m=4$

A) 3
B) 256
C) 44
D) 16

Question 23

Evaluate.

- $x^{1}$ , when $x=16$

A) 18
B) 32
C) 512
D) 16

Question 24

Evaluate.

- $p^{6}$ , when $p=0$

A) 0
B) 6
C) 1
D) 24

Question 25

Evaluate.

- $-p^{3}$ , when $p=4$

A) -64
B) 4
C) 12
D) 64

Question 26

Evaluate.

- $y^{13}$ when $y=1$

A) 0
B) 1
C) - 1
D) 13

Question 27

Evaluate.

- $x^{2}-9$ when $x=-5$

A) -14
B) 16
C) $x^{2}-5$
D) -56

Question 28

Evaluate.

- $y^{1}-5$ , when $y=-5$

A) -10
B) -5
C) 20
D) 0

Question 29

Evaluate.

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

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

Question 30

Evaluate.

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

A) $376.8 \mathrm{~cm}^{3}$
B) $565.2 \mathrm{~cm}^{3}$
C) $188.4 \mathrm{~cm}^{3}$
D) $2260.8 \mathrm{~cm}^{3}$

Question 31

Express using positive exponents. Then simplify.

- $2^{-4}$

A) $\frac{1}{8}$
B) - 16
C) 16
D) $\frac{1}{16}$

Question 32

Express using positive exponents. Then simplify.

- $(-5)^{-4}$

A) 625
B) -625
C) $\frac{1}{625}$
D) $-\frac{1}{625}$

Question 33

Express using positive exponents. Then simplify.

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

A) $\frac{1}{12}$
B) $-\frac{1}{81}$
C) - 81
D) 81

Question 34

Express using positive exponents. Then simplify.

- $x^{-2}$

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

Question 35

Express using positive exponents. Then simplify.

- $\frac{1}{\mathrm{x}^{-5}}$

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

Question 36

Express using positive exponents. Then simplify.

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

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

Question 37

Express using positive exponents. Then simplify.

- $\left(\frac{1}{5}\right)^{-3}$

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

Question 38

Express using positive exponents. Then simplify.

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

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

Question 39

Express the following using negative exponents.

- $\frac{1}{5^{4}}$

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

Question 40

Express the following using negative exponents.

- $\frac{1}{3^{9}}$

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

Question 41

Express the following using negative exponents.

- $\frac{1}{\mathrm{x}^{9}}$

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

Question 42

Express the following using negative exponents.

- $\frac{1}{b^{3}}$

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

Question 43

Express the following using negative exponents.

- $\frac{1}{t^{11}}$

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

Question 44

Multiply and simplify.

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

A) $3^{8}$
B) 8
C) 1
D) $3^{12}$

Question 45

Multiply and simplify.

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

A) $3^{2}$
B) 1
C) $3^{5}$
D) $3^{7}$

Question 46

Multiply and simplify.

- $5^{11} \cdot 5^{-3}$

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

Question 47

Multiply and simplify.

- $\mathrm{t}^{7} \cdot \mathrm{t}^{2}$

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

Question 48

Multiply and simplify.

- $y^{4} \cdot y^{0}$

A) $y^{40}$
B) $y^{4}$
C) 0
D) 1

Question 49

Multiply and simplify.

- $x \cdot x^{-8}$

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

Question 50

Multiply and simplify.

- $y^{-6} \cdot y^{-4}$

A) $\frac{1}{y^{10}}$
B) $\mathrm{y}^{10}$
C) $\frac{1}{y^{2}}$
D) $\frac{1}{y^{-10}}$

Question 51

Multiply and simplify.

- $a^{-8} \cdot a^{8}$

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

Question 52

Multiply and simplify.

- $x^{-9} \cdot x^{3} \cdot x^{-8}$

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

Question 53

Multiply and simplify.

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

A) $(3 x)^{12}$
B) $3 x^{7}$
C) $(3 x)^{7}$
D) $3 x^{12}$

Question 54

Multiply and simplify.

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

A) $2 x^{9} 2 y^{3}$
B) $x^{14} y^{2}$
C) $x^{9} y^{2}$
D) $x^{9} y^{3}$

Question 55

Multiply and simplify.

- $\left(mn^{4}\right)\left(m^{2} n^{7}\right)$

A) $m^{2} n^{11}$
B) $m^{2} n^{28}$
C) $2 m^{3} 2 n^{11}$
D) $m^{3} n^{11}$

Question 56

Divide and simplify.

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

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

Question 57

Divide and simplify.

- $\frac{(3 p)^{12}}{(3 p)^{8}}$

A) $81 p^{4}$
B) $\frac{p^{4}}{81}$
C) $\frac{81}{\mathrm{p}^{4}}$
D) $\frac{1}{81 p^{4}}$

Question 58

Divide and simplify.

- $\frac{(12 x)^{15}}{(12 x)^{15}}$

A) 1
B) $\frac{1}{\mathrm{x}^{15}}$
C) $x$
D) $x^{15}$

Question 59

Divide and simplify.

- $\frac{(26 x)^{5}}{(26 x)^{6}}$

A) $\frac{1}{26 x^{5}}$
B) $26 x$
C) $\frac{1}{26 x}$
D) $\frac{1}{\mathrm{x}^{5}}$

Question 60

Divide and simplify.

- $\frac{\mathrm{p}^{3}}{\mathrm{p}^{-5}}$

A) $p^{-2}$
B) $p^{-8}$
C) $\frac{1}{\mathrm{p}^{8}}$
D) $p^{8}$

Question 61

Divide and simplify.

- $\frac{t^{-2}}{t^{-6}}$

A) $\mathrm{t}^{4}$
B) $t^{-4}$
C) $t^{8}$
D) $t^{-8}$

Question 62

Divide and simplify.

- $\frac{\mathrm{z}^{-7}}{\mathrm{z}^{-5}}$

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

Question 63

Divide and simplify.

- $\frac{y^{-12}}{y^{2}}$

A) $y^{10}$
B) $y^{14}$
C) $\frac{1}{y^{14}}$
D) $\frac{1}{y^{-10}}$

Question 64

Divide and simplify.

- $\frac{t^{7}}{t}$

A) $\mathrm{t}^{7}$
B) $\frac{1}{t^{6}}$
C) $t^{6}$
D) $\mathrm{t}$

Question 65

Divide and simplify.

- $\frac{\mathrm{x}}{\mathrm{x}^{12}}$

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

Question 66

Simplify.

- $\left(8^{6}\right)^{-6}$

A) $8^{0}$
B) $-6 \cdot 8^{6}$
C) $\frac{1}{8^{36}}$
D) $8^{36}$

Question 67

Simplify.

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

A) $x^{-1}$
B) $\frac{1}{\mathrm{x}^{12}}$
C) $-4 x^{-3}$
D) $x^{12}$

Question 68

Simplify.

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

A) $(-5)^{16} \mathrm{a} ^{16}$
B) $(-5)^{16} \mathrm{a} ^{4}$
C) $-20 a^{4}$
D) $(-5) ^{4} \mathrm{a} ^{16}$

Question 69

Simplify.

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

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

Question 70

Simplify.

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

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

Question 71

Simplify.

- $-3\left(x^{-4} y^{-1}\right)^{-4}$

A) $\frac{-3}{x^{16} y^{4}}$
B) $(-3)^{4} x^{16} y ^{4}$
C) $-3 x^{16} y ^{4}$
D) $\frac{x^{16} y^{4}}{(-3)^{4}}$

Question 72

Simplify.

- $\left(-4 p^{5} q^{5} r^{5}\right)^{2}$

A) $(-4)^{2} p^{10} q^{10} r^{10}$
B) $(-4)^{10} p^{10} q^{10} r^{10}$
C) $(-4)^{2} p^{7} q^{7} r^{7}$
D) $-8 p^{7} q^{7} r^{7}$

Question 73

Simplify.

- $\left(-2 \mathrm{p}^{-2} \mathrm{q}^{2} \mathrm{r}^{-2}\right)^{6}$

A) $\frac{(-2){ }^{6} p^{12}}{q^{12} r^{12}}$
B) $(-2)^{6} p^{12} q^{12} r^{12}$
C) $\frac{(-2)^{6}}{\mathrm{p}^{12} \mathrm{q}^{12} \mathrm{r}^{12}}$
D) $\frac{(-2)^{6} q^{12}}{p^{12} r^{12}}$

Question 74

Simplify.

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

A) $\frac{2}{x^{2}}$
B) $\frac{4}{\mathrm{x}}$
C) $4 x^{2}$
D) $\frac{4}{x^{2}}$

Question 75

Simplify.

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

A) $\frac{27}{8 y^{3}}$
B) $\frac{27 y^{3}}{8}$
C) $\frac{27}{8 y}$
D) $\frac{27}{2 y^{3}}$

Question 76

Simplify.

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

A) $\frac{5 a^{4}}{81}$
B) $\frac{625 a}{81}$
C) $\frac{625 \mathrm{a}^{4}}{3}$
D) $\frac{625 \mathrm{a}^{4}}{81}$

Question 77

Simplify.

- $\left(\frac{\mathrm{a}^{2}}{\mathrm{~b}^{3}}\right)^{3}$

A) $\frac{a^{6}}{b^{3}}$
B) $\frac{a^{6}}{b^{9}}$
C) $\frac{\mathrm{a}^{9}}{\mathrm{~b}^{6}}$
D) $\frac{a^{3}}{b^{9}}$

Question 78

Simplify.

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

A) $\frac{a^{16}}{2}$
B) $\frac{x^{6}}{4}$
C) $\frac{x^{10}}{4}$
D) $\frac{x^{16}}{4}$

Question 79

Simplify.

- $\left(\frac{4}{b^{-3}}\right)^{4}$

A) $\frac{1}{256 b^{12}}$
B) 256 \{~b}^{12}
C) $\frac{256}{\mathrm{~b}^{12}}$
D) $\frac{\mathrm{b}^{12}}{256}$

Question 80

Simplify.

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

A) $\frac{x^{15} y^{5}}{z^{4}}$
B) $\frac{x^{5} y^{15}}{z^{20}}$
C) $\frac{x^{15} y^{5}}{z^{20}}$
D) $\frac{x^{8} y^{5}}{z^{9}}$