day 4 sept 12 lesson 1-3 laws of exponents.notebook · 2018. 9. 9. · day 4 sept 12 lesson 13 laws...

Day 4 sept 12 lesson 13 Laws of Exponents.notebook

1

September 12, 2017

Jun 191:12 PM


2

September 12, 2017

Sep 149:07 AM


3

September 12, 2017

Jun 191:35 PM


4

September 12, 2017

Sep 91:12 PM

Yesterday's answers


5

September 12, 2017

Sep 128:41 AM

Yesterday's answers


6

September 12, 2017

May 139:30 AM

Yesterday's answers


7

September 12, 2017

May 139:30 AM

Yesterday's answers


8

September 12, 2017

May 139:30 AM

Yesterday's answers


9

September 12, 2017

May 139:30 AM

Yesterday's answers


10

September 12, 2017

Sep 129:30 AM


11

September 12, 2017

May 139:30 AM

LAB Work:


12

September 12, 2017

Sep 149:08 AM


13

September 12, 2017

Sep 149:08 AM


14

September 12, 2017

Jun 191:35 PM


15

September 12, 2017

Jun 191:35 PM


16

September 12, 2017

Jun 191:35 PM


17

September 12, 2017

May 139:31 AM


18

September 12, 2017

Sep 91:15 PM


19

September 12, 2017

Sep 91:16 PM


20

September 12, 2017

Sep 91:18 PM


21

September 12, 2017

Sep 91:20 PM


22

September 12, 2017

May 139:32 AM


23

September 12, 2017

May 139:32 AM


24

September 12, 2017

May 139:33 AM


25

September 12, 2017

May 139:33 AM


26

September 12, 2017

May 139:33 AM


27

September 12, 2017

May 139:33 AM


28

September 12, 2017

May 139:33 AM

#1- 10, 12, 13,21,23Assignment: Pg 27


29

September 12, 2017

May 139:34 AM


30

September 12, 2017

Sep 129:14 AM


31

September 12, 2017

May 139:34 AM


32

September 12, 2017

May 139:34 AM


33

September 12, 2017

Sep 129:22 AM


34

September 12, 2017

Jun 191:39 PM

1

415

42

48

47

Simplify: 43 x 45

Answ

er

Exit Ticket


35

September 12, 2017

Jun 191:39 PM

2

52

521

54

510

Simplify: 57 ÷ 53

Answ

er


36

September 12, 2017

Jun 191:40 PM

3 Simplify:

Answ

er


37

September 12, 2017

Sep 91:16 PM

(Optional Extra Work)


38

September 12, 2017

Sep 91:20 PM

(Optional Extra Work)


39

September 12, 2017

Sep 91:21 PM


40

September 12, 2017

Jun 191:37 PM


41

September 12, 2017

Sep 91:13 PM

Attachments

12_Powers_and_Exponents.pdf

Write the expression using exponents.1. (–5)(–5)(–5)(–5)

SOLUTION: The base –5 is a factor 4 times, so the exponent is 4.

(–5)(–5)(–5)(–5) = (–5)4

2. 3 • 3 • 5 • q • q • q

SOLUTION: The base 3 is a factor 2 times, so its exponent is 2. The base 5 is a factor 1 time, so its exponent is 1. Because a number without an exponent is the same as a number with an exponent of 1, write 5 without an exponent. The base q is a factor 3 times, so its exponent is 3.

3 • 3 • 5 • q • q • q = 32 • 5 • q3

3. m • m • m • m • m

SOLUTION: The base m is a factor 5 times, so its exponent is 5.

m • m • m • m • m = m5

Evaluate the expression.

4. (–9)4

SOLUTION: Write the power as a product and multiply.

(–9)4 = (–9) • (–9) • (–9) • (–9) or 6,561

5.


or

6.


7. In the United States, nearly 8 • 109 text messages are sent every month. About how many text messages is this?


There are about 8 billion text messages sent in the United States each month.

8. Interstate 70 stretches almost 23 • 5

2 • 11 miles

across the United States. About how many miles long is Interstate 70?


Interstate 70 stretches for almost 2,200 miles.


9. g5 – h3 if g = 2 and h = 7

SOLUTION: Replace g with 2 and h with 7 in the expression

. Then write the powers as products and simplify.

10. c2 + d

3 if c = 8 and d = –3

SOLUTION: Replace c with 8 and d with –3 in the expression


11. a2 • b

6 if a = and b = 2

SOLUTION:

Replace a with and b with 2 in the expression


12. (r – s)3 + r2 if r = –3 and s = –4

SOLUTION: Replace r with –3 and s with –4 in the expression


13. Model with Mathematics Refer to the graphic novel frame below for Exercises a–c.

The metric system is based on powers of 10. For example, one kilometer is equal to 1,000 meters or

103 meters. Write each measurement in meters as a

power of 10. a. megameter (1,000,000 meters) b. gigameter (1,000,000,000 meters) c. petameter (1,000,000,000,000,000 meters)

SOLUTION: a. megameter: 1,000,000 meters has 6 zeros or

powers of 10. So, a megameter is 106.

b. gigameter: 1,000,000,000 meters has 9 zeros or

powers of 10. So, a gigameter is 109.

c. petameter: 1,000,000,000,000,000 meters has 15

zeros or powers of 10. So, a petameter is 1015

.

14. Identify Structure Write an expression with an exponent that has a value between 0 and 1.

SOLUTION:

Sample answer:

15. Identify Repeated Reasoning Describe the

following pattern: 34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3.

Then use a similar pattern to predict the value of 2–1

.

SOLUTION:

34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3

To go from 81 to 27, divide 81 by 3. This is the same for the rest of the values: 27 ÷ 3 = 9, and 9 ÷ 3 = 3.

To find the value of 2-1

, follow the same pattern.

23 = 8, 2

2 = 8 ÷ 2 or 4, 2

1 = 4 ÷ 2 or 2, 2

0 = 2 ÷ 2 or

1, 2-1 = 1 ÷ 2 or .

16. Which expression is equivalent to the expression below?

23 • 3

4

A. 3 • 3 • 4 • 4 • 4 B. 2 • 2 • 2 • 3 • 3 • 3 C. 2 • 2 • 2 • 3 • 3 • 3 • 3 D. 6 • 12

SOLUTION:

23 • 34 = 2 • 2 • 2 • 3 • 3 • 3 • 3. This corresponds to

choice C.

17. Write 3 · p ∙ p ∙ p · 3 · 3 using exponents.

SOLUTION: The base 3 is a factor 3 times, so its exponent is 4. The base p is a factor 3 times so its exponent is 3.

18. Evaluate x3 + y 4 if x = −3 and y = 4.

SOLUTION: Replace x with –3 and y with 4 in the expression


Write the expression using exponents.

19.

SOLUTION:

The base is a factor 3 times, so its exponent is

3.

20. s • (–7) • s • (–7) • (–7)

SOLUTION: Use the Commutative and Associative Properties to group the factors. The base –7 is a factor 3 times, soits exponent is 3. The base s is a factor 2 times, so itsexponent is 2.

21. 4 • b • b • 4 • b • b

SOLUTION: Use the Commutative and Associative Properties to group the factors. The base 4 is a factor 2 times, so its exponent is 2. The base b is a factor 4 times, so its exponent is 4.


22. k4 • m, if k = 3 and m =

SOLUTION:

Replace k with 3 and m with in the expression

k4 • m. Then write the powers as products and

simplify.

23. (c3 + d

4)2 – (c + d)

3, if c = –1 and d = 2

SOLUTION: Replace c with –1 and d with 2 in the expression

. Then write the powers as

products and simplify.

Replace the with , or = to make a true

statement.

24. (6 – 2)2 + 3 • 4 5

2

SOLUTION: Simplify each expression.

28 is larger than 25, so > will make the statement true.

(6 – 2)2 + 3 • 4 > 52

25. 5 + 72 + 33 34


81 is equal to 81, so = will make the statement true.

5 + 72 + 3

3 = 3

4

26.

SOLUTION: Write the powers as products and multiply.

is equal to , so = will make the statement

true.

=

27. Multiple Representations A square has a side length of s inches. a. Tables Copy and complete the table showing the side length, perimeter, and area of the square on a separate piece of paper.

b. Graphs On a separate piece of grid paper, graph the ordered pairs (side length, perimeter) and (side length, area) on the same coordinate plane. Then connect the points for each set. c. Words On a separate piece of paper, compare and contrast the graphs of the perimeter and area of the square. Which graph is a line?

SOLUTION: a. The perimeter of a square is found using the expression 4s. The area of a square is found using

the expression s2. Complete the table.

b. Graph the values from the table on the same coordinate plane. Side length is represented on the x-axis and both perimeter and area are represented on the y-axis.

c. Sample answer: The graph representing perimeter of a square is a line because each side length is multiplied by 4. The graph representing area of a square is nonlinear because each side length is squared. Squared values do not increase at a constant rate.

28. To find the volume of a cube, multiply its base, its height, and its width.

What is the volume of the cube expressed as a power?

A. 62 in

3

B. 63 in3

C. 64 in

3

D. 66 in3

SOLUTION: A cube has the same measures for all sides, so the base, height, and width are all 6 inches. The volume

is 6 • 6 • 6 or 63 inches cubed. This corresponds to

choice B.

29. Short Response The volume of an ice cube in

cubic millimeters is represented by the term 113.

What is 113 in standard form?

SOLUTION:

113 = 11 • 11 • 11 or 1,331

30. What is the value of x2 – y 4 if x = –3 and y = –2? F. –7 G. –2 H. 2 I. 7

SOLUTION:

Replace x with –3 and y with –2 in the expression x2 – y 4. Then write the powers as products and simplify.

The correct answer is F.

31. The table below shows the number of ants in an ant farm on different days. The number of ants doubles every ten days.

a. How many ants were in the farm on Day 1? b. How many ants will be in the farm on Day 91?

SOLUTION: a. Use the look for a pattern strategy. The number of ants doubles every 10 days, so going backward, the number of ants is halved each time the number ofdays is decreased by 10. Extend the pattern to find the number of ants on Day 1.

So, there were 10 ants in the farm on Day 1. b. Extend the pattern to find the number of ants in the farm on Day 91. The number of ants doubles every 10 days.

So, there will be 5,120 ants in the farm on Day 91.

Day 61 51 41 31 21 11 1 Number of ants

640 320 160 80 40 20 10

Day 51 61 71 81 91 Number of ants

320 640 1,280 2,560 5,120

32. Nieves and her three friends are playing a video game. The table shows their scores at the end of the first round.

a. What is the difference between the highest and lowest scores? b. By how many points is Nieves losing to Polly?

SOLUTION: a. The highest score is 230 points. The lowest score is –189. Subtract: 230 – (–189) = 230 + 189 or 419 The difference between the highest and lowest scores is 419 points. b. Nieves' score is –189. Polly's score is –142. Subtract: –142 – (–189) = –142 + 189 or 47 Polly is ahead of Nieves by 47 points.

Add.33. –12 + (–19)

SOLUTION: Since the signs are the same, add the numbers. The sign of the answer is the same as the sign of addends. –12 + (–19) = –31

34. –8 + (–11)


35. –5 + 6

SOLUTION: Since the signs are different, subtract the absolute values of the numbers. Since the largest absolute value is 6, the sign of the answer is the same as the sign of the 6. –5 + 6 = 1



(–5)(–5)(–5)(–5) = (–5)4

2. 3 • 3 • 5 • q • q • q


3 • 3 • 5 • q • q • q = 32 • 5 • q3

3. m • m • m • m • m


m • m • m • m • m = m5


4. (–9)4


(–9)4 = (–9) • (–9) • (–9) • (–9) or 6,561

5.


or

6.






2 • 11 miles





9. g5 – h3 if g = 2 and h = 7



10. c2 + d

3 if c = 8 and d = –3



11. a2 • b

6 if a = and b = 2

SOLUTION:



12. (r – s)3 + r2 if r = –3 and s = –4













.


SOLUTION:

Sample answer:



3 = 27, 3

2 = 9, 3

1 = 3.


.

SOLUTION:

34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3




23 = 8, 2

2 = 8 ÷ 2 or 4, 2

1 = 4 ÷ 2 or 2, 2

0 = 2 ÷ 2 or

1, 2-1 = 1 ÷ 2 or .


23 • 3

4

A. 3 • 3 • 4 • 4 • 4 B. 2 • 2 • 2 • 3 • 3 • 3 C. 2 • 2 • 2 • 3 • 3 • 3 • 3 D. 6 • 12

SOLUTION:


choice C.







19.

SOLUTION:


3.

20. s • (–7) • s • (–7) • (–7)


21. 4 • b • b • 4 • b • b



22. k4 • m, if k = 3 and m =

SOLUTION:



simplify.

23. (c3 + d

4)2 – (c + d)

3, if c = –1 and d = 2





statement.

24. (6 – 2)2 + 3 • 4 5

2



(6 – 2)2 + 3 • 4 > 52

25. 5 + 72 + 33 34



5 + 72 + 3

3 = 3

4

26.



true.

=









A. 62 in

3

B. 63 in3

C. 64 in

3

D. 66 in3



choice B.




SOLUTION:

113 = 11 • 11 • 11 or 1,331


SOLUTION:









640 320 160 80 40 20 10


320 640 1,280 2,560 5,120




Add.33. –12 + (–19)


34. –8 + (–11)


35. –5 + 6


eSolutions Manual - Powered by Cognero Page 1

1-2 Powers and Exponents



(–5)(–5)(–5)(–5) = (–5)4

2. 3 • 3 • 5 • q • q • q


3 • 3 • 5 • q • q • q = 32 • 5 • q3

3. m • m • m • m • m


m • m • m • m • m = m5


4. (–9)4


(–9)4 = (–9) • (–9) • (–9) • (–9) or 6,561

5.


or

6.






2 • 11 miles





9. g5 – h3 if g = 2 and h = 7



10. c2 + d

3 if c = 8 and d = –3



11. a2 • b

6 if a = and b = 2

SOLUTION:



12. (r – s)3 + r2 if r = –3 and s = –4













.


SOLUTION:

Sample answer:



3 = 27, 3

2 = 9, 3

1 = 3.


.

SOLUTION:

34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3




23 = 8, 2

2 = 8 ÷ 2 or 4, 2

1 = 4 ÷ 2 or 2, 2

0 = 2 ÷ 2 or

1, 2-1 = 1 ÷ 2 or .


23 • 3

4

A. 3 • 3 • 4 • 4 • 4 B. 2 • 2 • 2 • 3 • 3 • 3 C. 2 • 2 • 2 • 3 • 3 • 3 • 3 D. 6 • 12

SOLUTION:


choice C.







19.

SOLUTION:


3.

20. s • (–7) • s • (–7) • (–7)


21. 4 • b • b • 4 • b • b



22. k4 • m, if k = 3 and m =

SOLUTION:



simplify.

23. (c3 + d

4)2 – (c + d)

3, if c = –1 and d = 2





statement.

24. (6 – 2)2 + 3 • 4 5

2



(6 – 2)2 + 3 • 4 > 52

25. 5 + 72 + 33 34



5 + 72 + 3

3 = 3

4

26.



true.

=









A. 62 in

3

B. 63 in3

C. 64 in

3

D. 66 in3



choice B.




SOLUTION:

113 = 11 • 11 • 11 or 1,331


SOLUTION:









640 320 160 80 40 20 10


320 640 1,280 2,560 5,120




Add.33. –12 + (–19)


34. –8 + (–11)


35. –5 + 6




(–5)(–5)(–5)(–5) = (–5)4

2. 3 • 3 • 5 • q • q • q


3 • 3 • 5 • q • q • q = 32 • 5 • q3

3. m • m • m • m • m


m • m • m • m • m = m5


4. (–9)4


(–9)4 = (–9) • (–9) • (–9) • (–9) or 6,561

5.


or

6.






2 • 11 miles





9. g5 – h3 if g = 2 and h = 7



10. c2 + d

3 if c = 8 and d = –3



11. a2 • b

6 if a = and b = 2

SOLUTION:



12. (r – s)3 + r2 if r = –3 and s = –4













.


SOLUTION:

Sample answer:



3 = 27, 3

2 = 9, 3

1 = 3.


.

SOLUTION:

34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3




23 = 8, 2

2 = 8 ÷ 2 or 4, 2

1 = 4 ÷ 2 or 2, 2

0 = 2 ÷ 2 or

1, 2-1 = 1 ÷ 2 or .


23 • 3

4

A. 3 • 3 • 4 • 4 • 4 B. 2 • 2 • 2 • 3 • 3 • 3 C. 2 • 2 • 2 • 3 • 3 • 3 • 3 D. 6 • 12

SOLUTION:


choice C.







19.

SOLUTION:


3.

20. s • (–7) • s • (–7) • (–7)


21. 4 • b • b • 4 • b • b



22. k4 • m, if k = 3 and m =

SOLUTION:



simplify.

23. (c3 + d

4)2 – (c + d)

3, if c = –1 and d = 2





statement.

24. (6 – 2)2 + 3 • 4 5

2



(6 – 2)2 + 3 • 4 > 52

25. 5 + 72 + 33 34



5 + 72 + 3

3 = 3

4

26.



true.

=









A. 62 in

3

B. 63 in3

C. 64 in

3

D. 66 in3



choice B.




SOLUTION:

113 = 11 • 11 • 11 or 1,331


SOLUTION:









640 320 160 80 40 20 10


320 640 1,280 2,560 5,120




Add.33. –12 + (–19)


34. –8 + (–11)


35. –5 + 6






(–5)(–5)(–5)(–5) = (–5)4

2. 3 • 3 • 5 • q • q • q


3 • 3 • 5 • q • q • q = 32 • 5 • q3

3. m • m • m • m • m


m • m • m • m • m = m5


4. (–9)4


(–9)4 = (–9) • (–9) • (–9) • (–9) or 6,561

5.


or

6.






2 • 11 miles





9. g5 – h3 if g = 2 and h = 7



10. c2 + d

3 if c = 8 and d = –3



11. a2 • b

6 if a = and b = 2

SOLUTION:



12. (r – s)3 + r2 if r = –3 and s = –4













.


SOLUTION:

Sample answer:



3 = 27, 3

2 = 9, 3

1 = 3.


.

SOLUTION:

34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3




23 = 8, 2

2 = 8 ÷ 2 or 4, 2

1 = 4 ÷ 2 or 2, 2

0 = 2 ÷ 2 or

1, 2-1 = 1 ÷ 2 or .


23 • 3

4

A. 3 • 3 • 4 • 4 • 4 B. 2 • 2 • 2 • 3 • 3 • 3 C. 2 • 2 • 2 • 3 • 3 • 3 • 3 D. 6 • 12

SOLUTION:


choice C.







19.

SOLUTION:


3.

20. s • (–7) • s • (–7) • (–7)


21. 4 • b • b • 4 • b • b



22. k4 • m, if k = 3 and m =

SOLUTION:



simplify.

23. (c3 + d

4)2 – (c + d)

3, if c = –1 and d = 2





statement.

24. (6 – 2)2 + 3 • 4 5

2



(6 – 2)2 + 3 • 4 > 52

25. 5 + 72 + 33 34



5 + 72 + 3

3 = 3

4

26.



true.

=









A. 62 in

3

B. 63 in3

C. 64 in

3

D. 66 in3



choice B.




SOLUTION:

113 = 11 • 11 • 11 or 1,331


SOLUTION:









640 320 160 80 40 20 10


320 640 1,280 2,560 5,120




Add.33. –12 + (–19)


34. –8 + (–11)


35. –5 + 6




(–5)(–5)(–5)(–5) = (–5)4

2. 3 • 3 • 5 • q • q • q


3 • 3 • 5 • q • q • q = 32 • 5 • q3

3. m • m • m • m • m


m • m • m • m • m = m5


4. (–9)4


(–9)4 = (–9) • (–9) • (–9) • (–9) or 6,561

5.


or

6.






2 • 11 miles





9. g5 – h3 if g = 2 and h = 7



10. c2 + d

3 if c = 8 and d = –3



11. a2 • b

6 if a = and b = 2

SOLUTION:



12. (r – s)3 + r2 if r = –3 and s = –4













.


SOLUTION:

Sample answer:



3 = 27, 3

2 = 9, 3

1 = 3.


.

SOLUTION:

34 = 81, 3

3 = 27, 3

2 = 9, 3

1 = 3




23 = 8, 2

2 = 8 ÷ 2 or 4, 2

1 = 4 ÷ 2 or 2, 2

0 = 2 ÷ 2 or

1, 2-1 = 1 ÷ 2 or .


23 • 3

4

A. 3 • 3 • 4 • 4 • 4 B. 2 • 2 • 2 • 3 • 3 • 3 C. 2 • 2 • 2 • 3 • 3 • 3 • 3 D. 6 • 12

SOLUTION:


choice C.







19.

SOLUTION:


3.

20. s • (–7) • s • (–7) • (–7)


21. 4 • b • b • 4 • b • b



22. k4 • m, if k = 3 and m =

SOLUTION:



simplify.

23. (c3 + d

4)2 – (c + d)

3, if c = –1 and d = 2





statement.

24. (6 – 2)2 + 3 • 4 5

2



(6 – 2)2 + 3 • 4 > 52

25. 5 + 72 + 33 34



5 + 72 + 3

3 = 3

4

26.



true.

=









A. 62 in

3

B. 63 in3

C. 64 in

3

D. 66 in3



choice B.




SOLUTION:

113 = 11 • 11 • 11 or 1,331


SOLUTION:









640 320 160 80 40 20 10


320 640 1,280 2,560 5,120


a. What

day 4 sept 12 lesson 1-3 laws of exponents.notebook · 2018. 9. 9. · day 4 sept 12 lesson 13 laws...

Documents