Deck 5: Exponents, Polynomials, and Polynomial Functions

Question 1

Decide whether the expression has been simplified correctly.

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

Answer 1

True

Question 2

Decide whether the expression has been simplified correctly.

- $(a b)^{3}=a b^{3}$

Answer 2

False

Question 3

Decide whether the expression has been simplified correctly.

- $(2 b)^{4}=2^{4} b^{4}$

Answer 3

True

Question 4

Decide whether the expression has been simplified correctly.

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

Question 5

Decide whether the expression has been simplified correctly.

- $x^{4} \cdot x^{5}=x^{9}$

Question 6

Decide whether the expression has been simplified correctly.

- $x^{7} \cdot x^{6}=x^{42}$

Question 7

Decide whether the expression has been simplified correctly.

- $x y^{0}=x$

Question 8

Decide whether the expression has been simplified correctly.

- $\left(\frac{\mathrm{a}}{4}\right)^{9}=\frac{\mathrm{a}^{9}}{4^{9}}$

Question 9

Decide whether the expression has been simplified correctly.

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

Question 10

Apply the product rule for exponents, if possible.

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

A) $x^{48}$
B) $x^{14}$
C) $x^{15}$
D) $x^{12}$

Question 11

Apply the product rule for exponents, if possible.

- $y^{3} \cdot y^{6} \cdot y^{2}$

A) $y^{36}$
B) $y^{13}$
C) $y^{9}$
D) $y^{11}$

Question 12

Apply the product rule for exponents, if possible.

- $\left(-3 x^{5} y\right)\left(-4 x^{9} y^{2}\right)$

A) $12 x^{45} y^{2}$
B) $12 x^{14} y^{3}$
C) $12 x^{15} y^{3}$
D) $-12 x^{14} y^{2}$

Question 13

Apply the product rule for exponents, if possible.

- $\left(-2 x^{3}\right)\left(9 x^{10} y^{6}\right)$

A) $18 x^{13} y^{6}$
B) $-18 x^{30} y^{9}$
C) $-18 x^{30} y^{6}$
D) $-18 x^{13} y^{6}$

Question 14

Apply the product rule for exponents, if possible.

- $\mathrm{g}^{10} \cdot \mathrm{h}^{8}$

A) The product rule does not apply.
B) $\mathrm{gh}^{18}$
C) $\mathrm{g}^{80} \mathrm{~h}$
D) $\mathrm{gh}^{2}$

Question 15

Evaluate the expression.

- $13^{0}$

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

Question 16

Evaluate the expression.

- $-8^{0}$

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

Question 17

Evaluate the expression.

- $(-7)^{0}$

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

Question 18

Evaluate the expression.

- $7^{0}+9^{0}$

A) 2
B) 0
C) 16
D) 1

Question 19

Evaluate the expression.

- $(-11)^{0}+(-7)^{0}$

A) 0
B) -18
C) 2
D) -2

Question 20

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.

- $\mathrm{r}^{-3}$

A) $\mathrm{r}^{1 / 3}$

B) $\frac{1}{r^{3}}$

C) $-\frac{1}{r^{3}}$

D) $-r^{3}$

Question 21

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.

- $8^{-7}$

A) $-8^{1 / 7}$

B) $-\frac{1}{8^{7}}$

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

D) $-8^{7}$

Question 22

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.

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

A) $\frac{1}{9 p^{-3}}$

B) $\frac{1}{27 p^{3}}$

C) $\frac{1}{-9 p^{3}}$

D) $\frac{1}{3 p^{3}}$

Question 23

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.

- $(-\mathrm{a})^{-18}$

A) $\frac{1}{-a^{18}}$

B) $18 \mathrm{a}$

C) $\frac{1}{a^{-18}}$

D) $\frac{1}{a^{18}}$

Question 24

Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.

- $10^{-1}-4^{-1}$

A) $-\frac{1}{6}$

B) $-\frac{20}{3}$

C) $-\frac{3}{20}$

D) $\frac{3}{20}$

Question 25

Evaluate the expression.

- $\frac{7^{-3}}{5^{-2}}$

A) $\frac{343}{25}$

B) $\frac{2401}{125}$

C) $\frac{25}{343}$

D) $\frac{125}{2401}$

Question 26

Evaluate the expression.

- $\frac{1}{-3^{-2}}$

A) 3
B) -3
C) -9
D) 9

Question 27

Evaluate the expression.

- $\frac{1}{8^{-3}}$

A) 512
B) 4096
C) 64
D) 24

Question 28

Evaluate the expression.

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

A) $\frac{2401}{16}$

B) $-\frac{2401}{16}$

C) $\frac{16}{2401}$

D) $-\frac{16}{2401}$

Question 29

Evaluate the expression.

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

A) $\frac{27}{125}$

B) $\frac{125}{27}$

C) $-\frac{27}{125}$

D) $-\frac{125}{27}$

Question 30

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

- $\frac{x^{19}}{x^{5}}$

A) $x^{24}$
B) $x^{14}$
C) $\frac{1}{x^{14}}$
D) $-x^{14}$

Question 31

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

- $\frac{x^{5}}{x^{17}}$

A) $\frac{1}{x^{12}}$
B) $x^{12}$
C) $-x^{12}$
D) $\frac{1}{x^{22}}$

Question 32

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

- $\frac{x^{-17}}{x^{-8}}$

A) $\frac{1}{x^{25}}$

B) $\frac{1}{x^{9}}$

C) $x^{9}$

D) $-x^{25}$

Question 33

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

- $\frac{x^{-8}}{x^{-19}}$

A) $x^{11}$

B) $\frac{1}{x^{11}}$

C) $\frac{1}{x^{27}}$

D) $-x^{11}$

Question 34

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

- $\frac{x^{-16}}{x^{-16}}$

A) $x^{32}$
B) 1
C) $-x^{16}$
D) $\frac{1}{x^{32}}$

Question 35

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

- $\frac{6}{6^{-1}}$

A) The quotient rule does not apply.
B) $6^{2}$
C) 6
D) 1

Question 36

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.

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

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

B) $x^{4}$

C) $\frac{1}{y^{4}}$

D) The quotient rule does not apply.

Question 37

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers.

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

A) $\frac{1}{x^{9}}$

B) $x^{6}$

C) $x^{9}$

D) $\frac{1}{x^{6}}$

Question 38

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers.

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

A) $\frac{81 w^{9}}{x^{4}}$

B) $\frac{-81 w^{20}}{x^{4}}$

C) $\frac{-81 w^{20}}{x}$

D) $\frac{81 w^{20}}{x^{4}}$

Question 39

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $m^{-9} m^{5} m^{-1}$

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

B) $\mathrm{m}^{7}$

C) $\mathrm{m}^{5}$

D) $\frac{1}{m^{5}}$

Question 40

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(k^{-6}\right)^{8} k^{5}$

A) $\mathrm{k}^{43}$

B) $\frac{1}{\mathrm{k}^{7}}$

C) $\frac{1}{\mathrm{k}^{43}}$

D) $\mathrm{k}^{53}$

Question 41

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(6^{-1} \cdot 7^{-2}\right)^{-4}$

A) $6^{3} \cdot 7^{3}$

B) $\frac{1}{6^{3} \cdot 7^{3}}$

C) $6^{4} \cdot 7^{8}$

D) $\frac{1}{6^{4} \cdot 7^{8}}$

Question 42

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(7^{2} \cdot 4^{5}\right)^{-5}$

A) $7^{7} \cdot 4^{7}$

B) $7^{10} \cdot 4^{25}$

C) $\frac{1}{7^{7} \cdot 4^{7}}$

D) $\frac{1}{7^{10} \cdot 4^{25}}$

Question 43

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(5 x^{-4}\right)^{3}\left(x^{2}\right)^{-4}$

A) $5^{3} \mathrm{x}^{96}$

B) $\frac{1}{5^{-12} x^{20}}$

C) $\frac{5^{3}}{x^{20}}$

D) $\frac{5^{3}}{x^{3}}$

Question 44

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(x^{-2} y^{6}\right)^{-4}$

A) $\frac{1}{x^{8} y^{24}}$

B) $\frac{x^{-6}}{y^{2}}$

C) $\frac{y^{2}}{x^{-6}}$

D) $\frac{x^{8}}{y^{24}}$

Question 45

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}$

A) $\frac{7}{13 r^{2}}$

B) $\frac{7 \mathrm{r}^{19}}{13}$

C) $\frac{7 \mathrm{r}^{2}}{13}$

D) $\frac{7}{13 r^{19}}$

Question 46

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(\frac{11 t^{-2}}{t^{5}}\right)^{-3} \cdot \frac{3}{t^{-1}}$

A) $\frac{3 t^{2}}{11^{3}}$

B) $\frac{3 t^{21}}{11^{3}}$

C) $\frac{3 t^{22}}{11^{3}}$

D) $3 \cdot 11 \mathrm{t}^{22}$

Question 47

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\frac{\left(3 x^{4} y^{2}\right)^{6}}{9 x y^{2}}$

A) $\frac{x^{9} y^{6}}{3}$

B) $\frac{x^{23} y^{10}}{3}$

C) $81 x^{23} y^{10}$

D) $81 x^{9} y^{6}$

Question 48

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.

- $\left(\frac{2 x^{3} y^{-3}}{x^{-2} y^{4}}\right)^{-5}$

A) $\frac{y^{35}}{2 x^{25}}$

B) $\frac{y^{35}}{2 x^{5}}$

C) $\frac{2 x^{25}}{y^{35}}$

D) $\frac{y^{35}}{32 x^{25}}$

Question 49

For what values, if any, of $x(x \neq 0)$ and $n$ will $x^{-n}$ be a negative number?

Question 50

If $x \neq 0$ , explain the simplification of $\frac{x^{3 n}}{x^{n}}$ .

Question 51

Simplify the expressions $(2 x)^{0}$ and $\left(2 x^{0}\right)$ and explain how you arrived at your answers.

Question 52

Given that $0 < x <1$ and $x^{n}=y$ , explain why as $n$ becomes larger, $y$ becomes closer to 0 .

Question 53

Express the number in scientific notation

- $5,982,330$

A) $5.98233 \times 10^{6}$
B) $5.98233 \times 10^{-6}$
C) $5.98233 \times 10^{1}$
D) $5.98233 \times 10^{7}$

Question 54

Express the number in scientific notation

-845.3

A) $8.453 \times 10^{-3}$
B) $8.453 \times 10^{2}$
C) $8.453 \times 10^{-2}$
D) $8.453 \times 10^{3}$

Question 55

Express the number in scientific notation

-736.098

A) $7.36098 \times 10^{1}$
B) $7.36098 \times 10^{2}$
C) $7.36098 \times 10^{-1}$
D) $7.36098 \times 10^{-2}$

Question 56

Express the number in scientific notation

- $-67,000$

A) $-6.7 \times 10^{-5}$
B) $-6.7 \times 10^{5}$
C) $-6.7 \times 10^{-4}$
D) $-6.7 \times 10^{4}$

Question 57

Express the number in scientific notation

- $-8,300,000$

A) $-8.3 \times 10^{-5}$
B) $-8.3 \times 10^{5}$
C) $-8.3 \times 10^{-6}$
D) $-8.3 \times 10^{6}$

Question 58

Express the number in scientific notation

-0.000761

A) $7.61 \times 10^{-5}$
B) $7.61 \times 10^{-4}$
C) $7.61 \times 10^{-3}$
D) $7.61 \times 10^{4}$

Question 59

Express the number in scientific notation

-0.000087719

A) $8.7719 \times 10^{-5}$
B) $8.7719 \times 10^{4}$
C) $8.7719 \times 10^{5}$
D) $8.7719 \times 10^{-4}$

Question 60

Express the number in scientific notation

-0.0000011313

A) $1.1313 \times 10^{6}$
B) $1.1313 \times 10^{-5}$
C) $1.1313 \times 10^{-7}$
D) $1.1313 \times 10^{-6}$

Question 61

Express the number in scientific notation

-0.000000939012

A) $9.39012 \times 10^{7}$
B) $9.39012 \times 10^{-6}$
C) $9.39012 \times 10^{6}$
D) $9.39012 \times 10^{-7}$

Question 62

Express the number in scientific notation

-0.000000034603

A) $3.4603 \times 10^{-9}$
B) $3.4603 \times 10^{-8}$
C) $3.4603 \times 10^{-7}$
D) $3.4603 \times 10^{8}$

Question 63

Express the number in standard notation.

- $2.50 \times 10^{5}$

A) 250,000
B) $2,500,000$
C) 125
D) 25,000

Question 64

Express the number in standard notation.

- $1.090 \times 10^{5}$

A) 54.5
B) 109,000
C) 10,900
D) $1,090,000$

Question 65

Express the number in standard notation.

- $7.3714 \times 10^{6}$

A) 442.284
B) $73,714,000$
C) 737,140
D) $7,371,400$

Question 66

Express the number in standard notation.

- $2.89 \times 10^{-4}$

A) 0.0000289
B) $-289,000$
C) 0.000289
D) 0.00289

Question 67

Express the number in standard notation.

- $3.448 \times 10^{-5}$

A) $-344,800$
B) 0.00003448
C) 0.000003448
D) 0.0003448

Question 68

Express the number in standard notation.

- $8.213 \times 10^{-6}$

A) 0.000008213
B) 0.0000008213
C) 0.00008213
D) $-8,213,000$

Question 69

Express the number in standard notation.

- $4.0813 \times 10^{-7}$

A) 0.000000040813
B) $-408,130,000$
C) 0.0000040813
D) 0.00000040813

Question 70

Express the number in standard notation.

- $-7.695 \times 10^{5}$

A) $-7,695,000$
B) $-76,950$
C) $-76,950,000$
D) $-769,500$

Question 71

Find the value of the expression.

- $\frac{0.006 \times 2400}{4800}$

A) 0.0003
B) 0.003
C) 0.03
D) 30

Question 72

Find the value of the expression.

- $\frac{16,000 \times 0.09}{36,000}$

A) 0.04
B) 40,000
C) 0.4
D) 0.004

Question 73

Find the value of the expression.

- $\frac{420,000 \times 0.006}{0.07 \times 480,000}$

A) 0.75
B) 7.5
C) 0.075
D) 0.0075

Question 74

Find the value of the expression.

- $\frac{18 \times 10^{8}}{6 \times 10^{6}}$

A) -0.03
B) -300
C) 0.03
D) 300

Question 75

Find the value of the expression.

- $\frac{7 \times 10^{-3}}{28 \times 10^{2}}$

A) -0.0000025
B) 25,000
C) $-25,000$
D) 0.0000025

Question 76

Solve the problem. Express your answer in scientific notation, rounding as needed.

-The national debt of a small country is $\$ 6,460,000,000$ and the population is $2,586,000$ . What is the amount of debt per person?

A) $\$ 2.50 \times 10^{3}$
B) $\$ 2.50 \times 10^{2}$
C) $\$ 2.50 \times 10^{4}$
D) $\$ 2.50 \times 10^{6}$

Question 77

Solve the problem. Express your answer in scientific notation, rounding as needed.

-A computer can do one calculation in $1.4 \times 10^{-7}$ seconds. How long would it take the computer to do a trillion $\left(10^{12}\right)$ calculations?

A) $1.4 \times 10^{12} \mathrm{sec}$
B) $1.4 \times 10^{-7} \mathrm{sec}$
C) $1.4 \times 10^{6} \mathrm{sec}$
D) $1.4 \times 10^{5} \mathrm{sec}$

Question 78

Find the result that a calculator will give for the stated problem. Write your answer using the usual scientific notation.

- $(1.5 \mathrm{E} 15) *(5 \mathrm{E}-9)$

A) $-7.5 \times 10^{6}$
B) $7.5 \times 10^{6}$
C) $7.5 \times 10^{-6}$
D) $7.5 \times 10^{7}$

Question 79

Find the result that a calculator will give for the stated problem. Write your answer using the usual scientific notation.

-(7.2E17)/(3E-7)

A) $2.4 \times 10^{-24}$
B) $2.4 \times 10^{10}$
C) $21.6 \times 10^{24}$
D) $2.4 \times 10^{24}$

Question 80

In scientific notation, what is the largest integer which can be multiplied by a power of 10 ?

A) 10
B) -9
C) 1
D) 9