Deck 10: Polynomials: Operations

Question 1

What is the meaning of the expression?

- $5^{2}$

A) 7
B) 3
C) $2 \cdot 5$
D) $5 \cdot 5$

Answer 1

$5 \cdot 5$

Question 2

What is the meaning of the expression?

- $15^{2}$

A) 450
B) $2 \cdot 15$
C) 17
D) $15 \cdot 15$

Answer 2

$15 \cdot 15$

Question 3

What is the meaning of the expression?

-4⁶

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

Answer 3

$4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4$

Question 4

What is the meaning of the expression?

- $0.01^{3}$

A) $0.01 \cdot 0.01 \cdot 0.01$
B) $0.00000001$
C) $3 \cdot 0.01$
D) $0.000008$

Question 5

What is the meaning of the expression?

- $(-9.7)^{3}$

A) $(-9.7)(-9.7)(-9.7)$
B) $-9.7 \cdot 9.7 \cdot 9.7$
C) $3(-9.7)$
D) $(9.7)(9.7)(9.7)$

Question 6

What is the meaning of the expression?

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

A) $\frac{2 \cdot 2 \cdot 2 \cdot 2}{5}$
B) $\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)\left(\frac{2}{5}\right)$
C) $4\left(\frac{2}{5}\right)$
D) $\frac{2}{5 \cdot 5 \cdot 5 \cdot 5}$

Question 7

What is the meaning of the expression?

- $4 x^{3}$

A) $4 \cdot x \cdot x \cdot x$
B) $4 \cdot 4 \cdot 4 \cdot x$
C) $4 x \cdot 4 x \cdot 4 x$
D) $4 \cdot x \cdot 3$

Question 8

What is the meaning of the expression?

- $-4 q^{3}$

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

Question 9

Evaluate.

- $4^{0}$

A) 0
B) 1
C) 4
D) -1

Question 10

Evaluate.

--15⁰

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

Question 11

Evaluate.

- $(-10)^{0}$

A) -1
B) 0
C) -10
D) 1

Question 12

Evaluate.

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

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

Question 13

Evaluate.

- $(8 x)^{0} ; x \neq 0$

A) 1
B) 0
C) 8
D) $8 x$

Question 14

Evaluate.

- $a^{1}$

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

Question 15

Evaluate.

- $7.17^{1}$

A) 51.41
B) 1
C) 7.17
D) 0

Question 16

Evaluate.

- $\left(-\frac{3}{5}\right)^{0}$

A) 1
B) 0
C) -1
D) $\frac{3}{5}$

Question 17

Evaluate.

- $\left(\frac{4}{7}\right)^{1}$

A) $-\frac{4}{7}$
B) $\frac{4}{7}$
C) $\frac{7}{4}$
D) 1

Question 18

Evaluate.

- $x y^{1}$

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

Question 19

Evaluate.

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

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

Question 20

Evaluate.

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

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

Question 21

Evaluate.

- $m^{2}$ when $m=17$

A) 578
B) 19
C) 289
D) 34

Question 22

Evaluate.

- $m^{4}$ when $m=3$

A) 3
B) 34
C) 12
D) 81

Question 23

Evaluate.

- $x^{1}$ , when $x=15$

A) 17
B) 15
C) 30
D) 450

Question 24

Evaluate.

- $-\mathrm{p}^{4}$ , when $\mathrm{p}=6$

A) 1296
B) 5
C) 24
D) -1296

Question 25

Evaluate.

- $y^{11}$ when $y=1$

A) 11
B) 1
C) 0
D) -1

Question 26

Evaluate.

- $x^{2}-6$ when $x=-3$

A) $x^{2}-3$
B) -9
C) -27
D) 3

Question 27

Evaluate.

- $y^{1}-6$ , when $y=-2$

A) -32
B) -2
C) -6
D) -8

Question 28

The volume of a cube with sides of length s is given by V = s3. Find the volume of the cube.

A) $69 \mathrm{~m}^{3}$
B) $12,167 \mathrm{~m}^{3}$
C) $529 \mathrm{~m}^{3}$
D) $1058 \mathrm{~m}^{3}$

Question 29

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) $536.9 \mathrm{~m}^{3}$
B) $1208.1 \mathrm{~m}^{3}$
C) $4832.5 \mathrm{~m}^{3}$
D) $268.5 \mathrm{~m}^{3}$

Question 30

Express using positive exponents. Then simplify.

-4^-3

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

Question 31

Express using positive exponents. Then simplify.

-(-3)^-4

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

Question 32

Express using positive exponents. Then simplify.

--5^-4

A) - 625
B) $\frac{1}{20}$
C) $-\frac{1}{625}$
D) 625

Question 33

Express using positive exponents. Then simplify.

-x^-8

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

Question 34

Express using positive exponents. Then simplify.

- $\frac{1}{x^{-7}}$

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

Question 35

Express using positive exponents. Then simplify.

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

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

Question 36

Express using positive exponents. Then simplify.

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

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

Question 37

Express using positive exponents. Then simplify.

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

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

Question 38

Express the following using negative exponents.

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

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

Question 39

Express the following using negative exponents.

- $\frac{1}{2^{7}}$

A) $7-2$
B) $2^{-7}$
C) $2^{-8}$
D) $2^{7}$

Question 40

Express the following using negative exponents.

- $\frac{1}{x^{7}}$

A) $x^{-7}$
B) $7^{-x+1}$
C) $7^{-x}$
D) $x^{7}$

Question 41

Express the following using negative exponents.

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

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

Question 42

Express the following using negative exponents.

- $\frac{1}{t^{12}}$

A) $12^{t}$
B) $12^{-\mathrm{t}}$
C) $t^{12}$
D) $t^{-12}$

Question 43

Multiply and simplify.

- $3^{4} \cdot 3^{2}$

A) 1
B) 6
C) $3^{6}$
D) $3^{8}$

Question 44

Multiply and simplify.

- $3^{-4} \cdot 3^{7}$

A) 1
B) $3^{7}$
C) $3^{3}$
D) $3^{10}$

Question 45

Multiply and simplify.

- $5^{9} \cdot 5^{-2}$

A) $5^{2}$
B) $5^{9}$
C) $5^{5}$
D) $5^{7}$

Question 46

Multiply and simplify.

- $t^{8} \cdot t^{2}$

A) $\frac{1}{t^{6}}$
B) $\frac{1}{t^{10}}$
C) $\mathrm{t}^{6}$
D) $\mathrm{t}^{10}$

Question 47

Multiply and simplify.

- $y^{14} \cdot y^{0}$

A) 1
B) $\mathrm{y}^{140}$
C) 0
D) $y^{14}$

Question 48

Multiply and simplify.

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

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

Question 49

Multiply and simplify.

- $y^{-9} \cdot y^{-4}$

A) $\frac{1}{y^{13}}$
B) $\frac{1}{y^{-13}}$
C) $y^{13}$
D) $\frac{1}{y^{5}}$

Question 50

Multiply and simplify.

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

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

Question 51

Multiply and simplify.

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

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

Question 52

Multiply and simplify.

- $(3 x)^{0}(3 x)^{17}$

A) $(3 x)^{17}$
B) $(3 x)^{0}$
C) $3 x^{17}$
D) $3 x^{0}$

Question 53

Multiply and simplify.

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

A) $x^{7} y^{2}$
B) $x^{12} y^{2}$
C) $2 x^{7} 2 y^{3}$
D) $x^{7} y^{3}$

Question 54

Multiply and simplify.

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

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

Question 55

Divide and simplify.

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

A) $\frac{1}{t^{3}}$
B) $t^{-5}$
C) $\frac{t^{2}}{t^{3}}$
D) $\mathrm{t}^{3}$

Question 56

Divide and simplify.

- $\frac{(4 p)^{9}}{(4 p)^{6}}$

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

Question 57

Divide and simplify.

- $\frac{(9 x)^{15}}{(9 x)^{15}}$

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

Question 58

Divide and simplify.

- $\frac{(24 \mathrm{x})^{8}}{(24 \mathrm{x})^{9}}$

A) $\frac{1}{x^{8}}$
B) $\frac{1}{24 x}$
C) $\frac{1}{24 x^{8}}$
D) $24 x$

Question 59

Divide and simplify.

- $\frac{\mathrm{p}^{3}}{\mathrm{p}^{-4}}$

A) $p^{-7}$
B) $p^{-1}$
C) $p^{7}$
D) $\frac{1}{\mathrm{p}^{7}}$

Question 60

Divide and simplify.

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

A) $t^{9}$
B) $t^{-5}$
C) $t^{-9}$
D) $t^{5}$

Question 61

Divide and simplify.

- $\frac{z^{-7}}{z^{-3}}$

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

Question 62

Divide and simplify.

- $\frac{y^{-11}}{y^{4}}$

A) $y^{7}$
B) $\frac{1}{y^{-7}}$
C) $\frac{1}{y^{15}}$
D) $y^{15}$

Question 63

Divide and simplify.

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

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

Question 64

Divide and simplify.

- $\frac{x}{x^{13}}$

A) $\frac{1}{x^{12}}$
B) $x^{13}$
C) $x^{12}$
D) $\frac{1}{x^{13}}$

Question 65

Simplify.

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

A) 2⁰
B) $\frac{1}{2^{9}}$
C) $2^{9}$
D) $-3 \cdot 2^{3}$

Question 66

Simplify.

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

A) $-4 x^{-4}$
B) $x^{16}$
C) $\frac{1}{x^{16}}$
D) $x^{0}$

Question 67

Simplify.

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

A) $(-2)^{5} \mathrm{a} 10$
B) $-10 a^{2}$
C) $(-2)^{10} a_{a} 10$
D) $(-2)^{10} a^{2}$

Question 68

Simplify.

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

A) $(-5)^{4} x^{20} y^{4}$
B) $(-5)^{4} x^{9} y^{4}$
C) $-20 x^{5} y^{4}$
D) $-20 x^{5} y$

Question 69

Simplify.

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

A) $\frac{-3}{x^{12} y^{3}}$
B) $\frac{1}{(-3)^{3} x^{12} y^{3}}$
C) $-3 x^{12} y^{3}$
D) $-9 x^{4} y^{3}$

Question 70

Simplify.

- $-2\left(x^{-5} y-1\right)-4$

A) $(-2)^{4} \mathrm{x}^{20} \mathrm{y}^{4}$
B) $\frac{-2}{x^{20} y^{4}}$
C) $-2 x^{20} y^{4}$
D) $\frac{x^{20} y^{4}}{(-2)^{4}}$

Question 71

Simplify.

- $\left(-3 p^{4} q^{4} r^{4}\right)^{4}$

A) $(-3)^{4} \mathrm{p}^{16} \mathrm{q}^{16} \mathrm{r}_{\mathrm{r}} 16$
B) $(-3)^{4} p^{8} q^{8} r^{8}$
C) $(-3)^{16} \mathrm{p}^{16} \mathrm{q}^{16_{\mathrm{r}} 16}$
D) $-12 p^{8} q^{8} r^{8}$

Question 72

Simplify.

- $\left(-3 p^{-4} q^{4} r^{-4}\right)^{6}$

A) $\frac{(-3)^{6} q^{24}}{p^{24} r^{24}}$
B) $(-3)^{6} \mathrm{p}^{24} \mathrm{q}^{24} \mathrm{r} 24$
C) $\frac{(-3)^{6}}{p^{24} q^{24} r^{24}}$
D) $\frac{(-3)^{6} \mathrm{p}^{24}}{\mathrm{q}^{24} \mathrm{r}^{24}}$

Question 73

Simplify.

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

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

Question 74

Simplify.

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

A) $\frac{9}{4 y^{2}}$
B) $\frac{9}{4 y}$
C) $\frac{9}{2 y^{2}}$
D) $\frac{9 y^{2}}{4}$

Question 75

Simplify.

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

A) $\frac{5 a^{3}}{8}$
B) $\frac{125 a}{8}$
C) $\frac{125 a^{3}}{2}$
D) $\frac{125 a^{3}}{8}$

Question 76

Simplify.

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

A) $\frac{a^{12}}{b^{15}}$
B) $\frac{a^{12}}{b^{5}}$
C) $\frac{a^{5}}{b^{15}}$
D) $\frac{a^{15}}{b^{12}}$

Question 77

Simplify.

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

A) $\frac{a^{30}}{5}$
B) $\frac{x^{1}}{3125}$
C) $\frac{x^{30}}{3125}$
D) $\frac{x^{11}}{3125}$

Question 78

Simplify.

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

A) $\frac{3125}{b^{15}}$
B) $\frac{1}{3125 b^{15}}$
C) $3125 b^{15}$
D) $\frac{b^{15}}{3125}$

Question 79

Simplify.

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

A) $\frac{x^{20} y^{4}}{z^{16}}$
B) $\frac{x^{4} y^{20}}{z^{16}}$
C) $\frac{x^{20} y^{4}}{z^{4}}$
D) $\frac{x^{9} y^{4}}{z^{8}}$

Question 80

Simplify.

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

A) $\frac{x^{6}}{y^{7} z^{9}}$
B) $\frac{x^{9}}{y^{9} z^{18}}$
C) $\frac{x^{7}}{y^{9} z^{18}}$
D) $\frac{\mathrm{x}^{9}}{\mathrm{y}^{3} \mathrm{z}^{18}}$