Deck 5: Exponents, Polynomials, and Factoring Polynomials

Question 1

Choose the one alternative that best completes the statement or answers thequestion.

- $4^{4} \cdot 4^{5}$

A) $68,719,476,736$
B) 262,144
C) $1,099,511,627,776$
D) 524,288

Answer 1

262,144

Question 2

Choose the one alternative that best completes the statement or answers thequestion.

- $2^{4} \cdot 2$

A) 8
B) 64
C) 16
D) 32

Answer 2

32

Question 3

Choose the one alternative that best completes the statement or answers thequestion.

- $x^{4} \cdot x^{11}$

A) $(2 x)^{44}$
B) $(2 x)^{15}$
C) $x^{44}$
D) $x^{15}$

Answer 3

$x^{15}$

Question 4

Choose the one alternative that best completes the statement or answers thequestion.

- $m^{17} \cdot m^{21}$

A) $38 \mathrm{~m}$
B) $\mathrm{m}^{357}$
C) $\mathrm{m}^{4}$
D) $\mathrm{m}^{38}$

Question 5

Choose the one alternative that best completes the statement or answers thequestion.

- $a^{2} \cdot a^{3} \cdot a^{9}$

A) a12
B) $a^{14}$
C) $a^{5}$
D) $\mathrm{a}^{15}$

Question 6

Choose the one alternative that best completes the statement or answers thequestion.

- $(x-6)^{11} \cdot(x-6)^{3}$

A) $(2 x-12 x+36)^{33}$
B) $(x-6)^{14}$
C) $(x-6)^{33}$
D) $(2 x-12)^{14}$

Question 7

Choose the one alternative that best completes the statement or answers thequestion.

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

A) $7 x^{10} y^{8}$
B) $12 x^{24} y ^{16}$
C) $12 x^{10} y^{8}$
D) $7 x^{24} y ^{16}$

Question 8

Choose the one alternative that best completes the statement or answers thequestion.

- $\left(a^{4}\right)^{8}$

A) $a^{32}$
B) $a^{8}$
C) $a^{14}$
D) $a^{12}$

Question 9

Choose the one alternative that best completes the statement or answers thequestion.

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

A) 12
B) 7
C) 64
D) 32

Question 10

Choose the one alternative that best completes the statement or answers thequestion.

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

A) $2 x^{27}$
B) $x^{54}$
C) $x^{180}$
D) $x^{27}$

Question 11

Choose the one alternative that best completes the statement or answers thequestion.

- $\left(2 x^{9}\right)^{4}$

A) $16 x^{9}$
B) $16 x^{13}$
C) $2 x^{36}$
D) $16 x^{36}$

Question 12

Choose the one alternative that best completes the statement or answers thequestion.

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

A) $49 x^{8}$
B) $7 x^{2}$
C) $7 x^{4}$
D) $49 x^{4}$

Question 13

Choose the one alternative that best completes the statement or answers thequestion.

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

A) $36 x^{24}$
B) $36 x^{10}$
C) $46,656 x^{24}$
D) $6 x^{24}$

Question 14

Choose the one alternative that best completes the statement or answers thequestion.

- $\left(x^{4} y^{9}\right)^{3}$

A) $x^{64} y^{ 729}$
B) $x^{7} y^{12}$
C) $x^{4} y ^{27}$
D) $x^{12} y^{27}$

Question 15

Choose the one alternative that best completes the statement or answers thequestion.

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

A) $3 x^{4} y^ 6$
B) $9 x^{4} y^{6}$
C) $9 x ^4 y^{5}$
D) $3 x^{4} y^{5}$

Question 16

Choose the one alternative that best completes the statement or answers thequestion.

- $\left(x^{7} y^{9} z^{8}\right)^{4}\left(x^{5} y^{10} z^{12}\right)^{4}$

A) $x^{48} y^{76} z^{80}$
B) $x^{96} {y} ^{152}z^{ 160}$
C) $2 x^{48} 2 y^{76} 2 z ^{80}$
D) $x^{560}{y} ^{1440 }z^{ 1536}$

Question 17

Simplify. (A ssume all variables are nonzero.)

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

A) $x^{1.8}$
B) $x^{3}$
C) $x^{11}$
D) 1.8

Question 18

Simplify. (A ssume all variables are nonzero.)

- $\mathrm{z}^{35} \div \mathrm{z}^{5}$

A) $z^{7}$
B) $z^{30}$
C) $z^{40}$
D) $z^{175}$

Question 19

Simplify. (A ssume all variables are nonzero.)

- $\frac{8 y^{3}}{4 y}$

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

Question 20

Simplify. (A ssume all variables are nonzero.)

- $\frac{(a-7 b)^{20}}{(a-7 b)^{10}}$

A) $(a-7 b)^{10}$
B) $(\mathrm{a}-7 \mathrm{~b})^{200}$
C) $(\mathrm{a}-7 \mathrm{~b})^{30}$
D) $(\mathrm{a}-7 \mathrm{~b})^{2}$

Question 21

Simplify. (A ssume all variables are nonzero.)

- $\frac{(4 x-10)^{10}}{(4 x-10)^{5}}$

A) $(4 \mathrm{x}-10)^{5}$
B) 1
C) $(4 x-10)^{15}$
D) $(4 \mathrm{x}-10)^{50}$

Question 22

Simplify. (A ssume all variables are nonzero.)

- $\frac{a^{7} b^{3}}{a^{2} b}$

A) $a^{14} b^{3}$
B) $\frac{21}{2}$
C) $\mathrm{a}^{5} \mathrm{~b}^{2}$
D) $(\mathrm{ab})^{12}$

Question 23

Simplify. (A ssume all variables are nonzero.)

- $\frac{15 x^{8} y^{4} z^{7}}{3 x^{4} y^{4} z^{2}}$

A) $5 x^{32} z^{14}$
B) $12 x^{4} z^{5}$
C) $5 x^{12} z^{9}$
D) $5 x^{4} z^{5}$

Question 24

Simplify. (A ssume all variables are nonzero.)

- $8^0$

A) 1
B) 8
C) 0
D) - 1

Question 25

Simplify. (A ssume all variables are nonzero.)

- $-3^0$

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

Question 26

Simplify. (A ssume all variables are nonzero.)

- $(-9)^{0}$

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

Question 27

Simplify. (A ssume all variables are nonzero.)

- $\frac{4}{70}$

A) 1
B) 0
C) 4
D) $\frac{4}{7}$

Question 28

Simplify. (A ssume all variables are nonzero.)

- $\left(\frac{6}{19}\right)^{0}$

A) - 1
B) $\frac{6}{19}$
C) 0
D) 1

Question 29

Simplify. (A ssume all variables are nonzero.)

- $(13 \mathrm{x})^{0}$

A) 13
B) $13 x$
C) 0
D) 1

Question 30

Simplify. (A ssume all variables are nonzero.)

- $\left(16 x^{6} y^{8} z^{5}\right)^{0}$

A) 0
B) $16 x ^{6} y^{8} z^{5}$
C) 1
D) 16

Question 31

Simplify. (A ssume all variables are nonzero.)

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

A) $2 \frac{3}{4}$

B) $\frac{9}{16}$

C) $\frac{16}{9}$

D) $\frac{9}{4}$

Question 32

Simplify. (A ssume all variables are nonzero.)

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

A) $\frac{x}{25}$

B) $\frac{x^{2}}{5}$

C) $\frac{x^{2}}{25}$

D) $25 x^{2}$

Question 33

Simplify. (A ssume all variables are nonzero.)

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

A) $\frac{2}{x^{3}}$

B) $8 x^{3}$

C) $\frac{8}{x^{3}}$

D) $\frac{8}{x}$

Question 34

Simplify. (A ssume all variables are nonzero.)

- $\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{6}$

A) $\frac{a^{6}}{b^{6}}$

B) $\frac{6 a}{6 b}$

C) 6

D) $\frac{a^{6}}{b}$

Question 35

Simplify. (A ssume all variables are nonzero.)

- $\left(\frac{\mathrm{a}^{3}}{\mathrm{~b}^{4}}\right)^{2}$

A) $\frac{a^{6}}{b^{8}}$

B) $\frac{a^{6}}{b^{4}}$

C) $\frac{a^{8}}{b^{6}}$

D) $\frac{a^{4}}{b^{8}}$

Question 36

Simplify. (A ssume all variables are nonzero.)

- $\left(\frac{5 x^{6} y^{2}}{7 z^{6}}\right)^{3}$

A) $\frac{125 x^{18} y^{6}}{343 z^{18}}$

B) $\frac{125 x^{18} y^ 5}{343 z^{18}}$

C) $\frac{125 x^{9} y^{5}}{343 z^{9}}$

D) $\frac{125 x^{18} y^{6}}{7 z^{9}}$

Question 37

Simplify. (A ssume all variables are nonzero.)

- $\left(\frac{2 \mathrm{a}^{3} \mathrm{~b}^{3}}{\mathrm{c}^{4}}\right)^{3}$

A) $\frac{8 a^{9} b^{9}}{c^{12}}$

B) $\frac{2 a^{9} b^{9}}{c^{12}}$

C) $\frac{2 \mathrm{a}^{9} \mathrm{~b}^{9}}{\mathrm{c}^{7}}$

D) $\frac{8 a^{6} b^{6}}{c^{7}}$

Question 38

Simplify. (A ssume all variables are nonzero.)

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

A) $\frac{x^{12}}{y^{3} z^{28}}$

B) $\frac{x^{12}}{y^{7} z^{28}}$

C) $\frac{x^{12}}{y^{12} z^{28}}$

D) $\frac{x^{7}}{y^{8} z^{11}}$

Question 39

Simplify. (A ssume all variables are nonzero.)

- $\left(\frac{a^{3} b^{6}}{b^{2} c^{3}}\right)^{6}$

A) $\frac{a^{18}}{c^{18}}$

B) 0

C) $\frac{a^{18} b^{24}}{c^{18}}$

D) $\frac{\mathrm{a}^{9} \mathrm{~b}^{24}}{\mathrm{c}^{9}}$

Question 40

Find the missing factor or exponent(s).

- $x^{7} \cdot ?=x^{15}$

A) $x^{16}$
B) $x^{24}$
C) $x^{8}$
D) $x^{7}$

Question 41

Find the missing factor or exponent(s).

- $\left(\mathrm{x}^{?}\right)^{3}=\mathrm{x}^{39}$

A) 36
B) 3
C) 13
D) 26

Question 42

Find the missing factor or exponent(s).

- $\left(\mathrm{x}^{3}\right)^{?}=\mathrm{x}^{27}$

A) 9
B) 18
C) 27
D) 24

Question 43

Find the missing factor or exponent(s).

- $\left(x^{7}\right)^{?} \cdot\left(x^{9}\right)^{3}=x^{62}$

A) 35
B) 5
C) 21
D) 7

Question 44

Find the missing factor or exponent(s).

- $\left(x^{?} \cdot y^{?}\right)^{6}=x^{18} y^{5}$

A) 3,9
B) 6,9
C) 3, 6
D) 12,48

Question 45

Find the missing factor or exponent(s).

- $\left(-3 a ? a^{3} ?\right)^{3}=-27 a^{18} b^{12}$

A) 4,6
B) 6,4
C) 9,7
D) 7,9

Question 46

Find the missing factor or exponent(s).

- $\frac{x^{10} y^{2} ?}{x^{?} y^{19}}=x^{4} y^{6}$

A) 19,10
B) 6,25
C) 10,6
D) 6, 19

Question 47

Find the missing factor or exponent(s).

- $\left(\frac{x^{10} y^{7}}{z^{8}}\right)^{?}=\frac{x^{50} y^{35}}{z^{40}}$

A) 7
B) 8
C) 10
D) 5

Question 48

Evaluate the given function

- $g(x)=x^{5}, g(8)$

A) 40
B) $8 x^{5}$
C) $x^{40}$
D) 32,768

Question 49

Evaluate the given function

- $f(x)=x^{3}, f(-5)$

A) $-5 x^{3}$
B) -125
C) -15
D) $x^{-15}$

Question 50

Evaluate the given function

- $f(x)=x^{6}, f(-1)$

A) -1
B) $-\mathrm{x}$
C) 0
D) 1

Question 51

Evaluate the given function

- $f(x)=x^{7}, f\left(b^{3}\right)$

A) $b^{10}$
B) 21
C) $x^{7} b^{3}$
D) $b^{21}$

Question 52

The number of feet traveled by a free-falling object in $t$ seconds is given by the function $f(t)=16 t^{2}$ . How far would it fall in 9 seconds?

A) 18 feet
B) 81 feet
C) 144 feet
D) 1296 feet

Question 53

The area of a square with side $x$ is given by the function $A(x)=x^{2}$ . Find the area of a square if each side is 30 feet long.

A) 120 square feet
B) 60 square feet
C) 900 square feet
D) 90 square feet

Question 54

The area of a circle with radius $r$ is given by the function $A(r)=\pi r^{2}$ . Find the area of the base of a circular storage tank if the radius is 5 feet long. Use $\pi \approx 3.14$ .

A) 15.7 square feet
B) 31.4 square feet
C) 78.5 square feet
D) 75 square feet

Question 55

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $3^{-2}$

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

Question 56

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

-2- 4

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

Question 57

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $x^{-2}$

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

Question 58

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $3 x^{-5}$

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

Question 59

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $-5 m^{-4}$

A) $-\frac{1}{625 m^{4}}$

B) $\frac{1}{625 m^{4}}$

C) $-\frac{5}{m^{4}}$

D) $\frac{625}{m^{4}}$

Question 60

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $\frac{1}{\mathrm{x}^{-4}}$

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

Question 61

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $\frac{5 x^{-6}}{y^{-2} z^{7}}$

A) $\frac{y^{2}}{5 x^{6} z^{7}}$

B) $\frac{5 y^{2}}{x^{6} z^{7}}$

C) $\frac{5 x^{6}}{y^{2} z^{7}}$

D) $\frac{5}{x^{6} y^{2} z^{7}}$

Question 62

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $\frac{a^{6}}{b^{-4}}$

A) 1
B) $\left(\frac{a}{b}\right)^{2}$
C) $\frac{b^{4}}{a^{6}}$
D) $a^{6} b^{4}$

Question 63

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $\frac{x^{-7}}{y^{-8}}$

A) $x y^{-15}$

B) $\frac{y^{8}}{x^{7}}$

C) $\frac{1}{x^{7} y^{8}}$

D) $x^{7} y^{8}$

Question 64

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)

- $\frac{9 a^{-3} b^{-8}}{c^{-3} d^{4}}$

A) $\frac{1}{9 a^{3} b^{8} c^{3} d^{4}}$

B) $\frac{9 c^{3} d^{4}}{a^{3} b^{8}}$

C) $\frac{9 c^{3}}{a^{3} b^{8} d^{4}}$

D) $\frac{c^{3}}{9 a^{3} b^{8} d^{4}}$

Question 65

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $x^{12} \cdot x^{-5}$

A) 7
B) $\frac{x^{12}}{x^{5}}$
C) $x^{7}$
D) $x^{17}$

Question 66

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $y^{-6} \cdot y^{-5}$

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

Question 67

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $\left(n^{9}\right)^{-2}$

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

Question 68

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

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

Question 69

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

A) $\frac{y^{4}}{x^{-4}}$

B) $\frac{1}{x^{4} y^{12}}$

C) $\frac{x^{-4}}{y^{4}}$

D) $\frac{x^{4}}{y^{12}}$

Question 70

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $\left(3 m^{4} n^{-2}\right)^{2}$

A) $\frac{3 m^{8}}{n^{4}}$
B) $3 m^{8} n^{4}$
C) $9 m^{8} n^{4}$
D) $\frac{9 m^{8}}{n^{4}}$

Question 71

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

A) $\frac{x^{20} y^{20}}{243 z 15}$

B) 0

C) $\frac{3 x^{20} y^{20}}{z^{15}}$

D) $\frac{x^{20} y^{20}}{z^{15}}$

Question 72

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

A) $\frac{t^{6}}{t^{2}}$

B) $t^{2}$

C) $\frac{1}{t^{2}}$

D) $t^{-8}$

Question 73

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

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

Question 74

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $\frac{x^{-3}}{x^{-8}}$

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

Question 75

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

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

Question 76

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $\frac{y^{-11}}{y^{2}}$

A) $\mathrm{y}^{9}$
B) $y^{13}$
C) $\frac{1}{y^{9}}$
D) $\frac{1}{y^{13}}$

Question 77

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $\frac{x^{4} x^{-9}}{x^{-5}}$

A) $\frac{x^{4} x^{5}}{x^{9}}$
B) 1
C) -1
D) 0

Question 78

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

A) $\frac{x^{4}}{81 y^{4}}$

B) $\frac{3 y^{4}}{x^{4}}$

C) $-\frac{x^{4}}{81 y^{4}}$

D) $\frac{81 y^{4}}{x^{4}}$

Question 79

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

- $\left(\frac{7 x^{-4}}{8 y^{-4}}\right)^{-2}$

A) $\frac{49 x^{42}}{64 y^{ 42}}$

B) $\frac{49 x^{8}}{64 y^{8}}$

C) $\frac{64 y^{8}}{49 x^{8}}$

D) $\frac{64 x^{8}}{49 y^{8}}$

Question 80

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)

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

A) $\frac{w z^{20}}{x^{16} y^{16}}$

B) $\frac{x^{16} y^{16}}{w^{4} z^{20}}$

C) $x^{16} y^{16} w^{4} z^{20}$

D) $\frac{w^{4} z^{20}}{x^{16} y^{16}}$