<< Chapter < Page Chapter >> Page >

7 6 4 2 + 1 5 Evaluate the exponential forms, moving left to right. 7 6 16 + 1 Multiply 7 and 6: 7 6 = 42 42 16 + 1 Subtract 16 from 42: 42 16 = 26 26 + 1 Add 26 and 1: 26 + 1 = 27 27

Got questions? Get instant answers now!

6 ( 3 2 + 2 2 ) + 4 2 Evaluate the exponential forms in the parentheses: 3 2 = 9  and  2 2 = 4 6 ( 9 + 4 ) + 4 2 Add the 9 and 4 in the parentheses: 9 + 4 = 13 6 ( 13 ) + 4 2 Evaluate the exponential form: 4 2 = 16 6 ( 13 ) + 16 Multiply 6 and 13: 6 13 = 78 78 + 16 Add 78 and 16: 78 + 16 = 94 94

Got questions? Get instant answers now!

6 2 + 2 2 4 2 + 6 2 2 + 1 3 + 8 2 10 2 19 5 size 12{ { {6 rSup { size 8{2} } +2 rSup { size 8{2} } } over {4 rSup { size 8{2} } +6 cdot 2 rSup { size 8{2} } } } + { {1 rSup { size 8{3} } +8 rSup { size 8{2} } } over {"10" rSup { size 8{2} } -"19" cdot 5} } } {} Recall that the bar is a grouping symbol. The fraction 6 2 + 2 2 4 2 + 6 2 2 size 12{ { {6 rSup { size 8{2} } +2 rSup { size 8{2} } } over {4 rSup { size 8{2} } +6 cdot 2 rSup { size 8{2} } } } } {} is equivalent to ( 6 2 + 2 2 ) ÷ ( 4 2 + 6 2 2 ) size 12{ \( 6 rSup { size 8{2} } +2 rSup { size 8{2} } \) ÷ \( 4 rSup { size 8{2} } +6 cdot 2 rSup { size 8{2} } \) } {} 36 + 4 16 + 6 4 + 1 + 64 100 19 5 size 12{ { {"36"+4} over {"16"+6 cdot 4} } + { {1+"64"} over {"100"-"19" cdot 5} } } {} 36 + 4 16 + 24 + 1 + 64 100 95 size 12{ { {"36"+4} over {"16"+"24"} } + { {1+"64"} over {"100"-"95"} } } {} 40 40 + 65 5 size 12{ { {"40"} over {"40"} } + { {"65"} over {5} } } {} 1 + 13 size 12{1+"13"} {} 14 size 12{"14"} {}

Got questions? Get instant answers now!

Practice set c

Determine the value of each of the following.

8 + ( 32 7 ) size 12{8+ \( "32"-7 \) } {}

33

Got questions? Get instant answers now!

( 34 + 18 2 3 ) + 11 size 12{ \( "34"+"18"-2 cdot 3 \) +"11"} {}

57

Got questions? Get instant answers now!

8 ( 10 ) + 4 ( 2 + 3 ) ( 20 + 3 15 + 40 5 ) size 12{8 \( "10" \) +4 \( 2+3 \) - \( "20"+3 cdot "15"+"40"-5 \) } {}

0

Got questions? Get instant answers now!

5 8 + 4 2 2 2 size 12{5 cdot 8+4 rSup { size 8{2} } -2 rSup { size 8{2} } } {}

52

Got questions? Get instant answers now!

4 ( 6 2 3 3 ) ÷ ( 4 2 4 ) size 12{4 \( 6 rSup { size 8{2} } -3 rSup { size 8{3} } \) ÷ \( 4 rSup { size 8{2} } -4 \) } {}

3

Got questions? Get instant answers now!

( 8 + 9 3 ) ÷ 7 + 5 ( 8 ÷ 4 + 7 + 3 5 ) size 12{ \( 8+9 cdot 3 \) ÷7+5 cdot \( 8÷4+7+3 cdot 5 \) } {}

125

Got questions? Get instant answers now!

3 3 + 2 3 6 2 29 + 5 8 2 + 2 4 7 2 3 2 ÷ 8 3 + 1 8 2 3 3 size 12{ { {3 rSup { size 8{3} } +2 rSup { size 8{3} } } over {6 rSup { size 8{2} } -"29"} } +5 left ( { {8 rSup { size 8{2} } +2 rSup { size 8{4} } } over {7 rSup { size 8{2} } -3 rSup { size 8{2} } } } right )÷ { {8 cdot 3+1 rSup { size 8{8} } } over {2 rSup { size 8{3} } -3} } } {}

7

Got questions? Get instant answers now!

Calculators

Using a calculator is helpful for simplifying computations that involve large num­bers.

Sample set d

Use a calculator to determine each value.

9, 842 + 56 85 size 12{9,"842"+"56" cdot "85"} {}

Key Display Reads
Perform the multiplication first. Type 56 56
Press × 56
Type 85 85
Now perform the addition. Press + 4760
Type 9842 9842
Press = 14602

The display now reads 14,602.

Got questions? Get instant answers now!

42 ( 27 + 18 ) + 105 ( 810 ÷ 18 ) size 12{"42" \( "27"+"18" \) +"105" \( "810"÷"18" \) } {}

Key Display Reads
Operate inside the parentheses Type 27 27
Press + 27
Type 18 18
Press = 45
Multiply by 42. Press × 45
Type 42 42
Press = 1890

Place this result into memory by pressing the memory key.

Key Display Reads
Now operate in the other parentheses. Type 810 810
Press ÷ 810
Type 18 18
Press = 45
Now multiply by 105. Press × 45
Type 105 105
Press = 4725
We are now ready to add these two quantities together. Press + 4725
Press the memory recall key. 1890
Press = 6615

Thus, 42 ( 27 + 18 ) + 105 ( 810 ÷ 18 ) = 6, 615 size 12{"42" \( "27"+"18" \) +"105" \( "810"÷"18" \) =6,"615"} {}

Got questions? Get instant answers now!

16 4 + 37 3 size 12{"16" rSup { size 8{4} } +"37" rSup { size 8{3} } } {}

Nonscientific Calculators
Key Display Reads
Type 16 16
Press × 16
Type 16 16
Press × 256
Type 16 16
Press × 4096
Type 16 16
Press = 65536
Press the memory key
Type 37 37
Press × 37
Type 37 37
Press × 1396
Type 37 37
Press × 50653
Press + 50653
Press memory recall key 65536
Press = 116189
Calculators with y x Key
Key Display Reads
Type 16 16
Press y x size 12{y rSup { size 8{x} } } {} 16
Type 4 4
Press = 4096
Press + 4096
Type 37 37
Press y x size 12{y rSup { size 8{x} } } {} 37
Type 3 3
Press = 116189

Thus, 16 4 + 37 3 = 116 , 189 size 12{"16" rSup { size 8{4} } +"37" rSup { size 8{3} } ="116","189"} {}

We can certainly see that the more powerful calculator simplifies computations.

Got questions? Get instant answers now!

Nonscientific calculators are unable to handle calculations involving very large numbers.

85612 21065 size 12{"85612" cdot "21065"} {}

Key Display Reads
Type 85612 85612
Press × 85612
Type 21065 21065
Press =

This number is too big for the display of some calculators and we'll probably get some kind of error message. On some scientific calculators such large numbers are coped with by placing them in a form called "scientific notation." Others can do the multiplication directly. (1803416780)

Got questions? Get instant answers now!

Practice set d

Use a calculator to find each value.

9, 285 + 86 ( 49 ) size 12{9,"285"+"86" \( "49" \) } {}

13,499

Got questions? Get instant answers now!

55 ( 84 26 ) + 120 ( 512 488 ) size 12{"55" \( "84"-"26" \) +"120" \( "512"-"488" \) } {}

6,070

Got questions? Get instant answers now!

106 3 17 4 size 12{"106" rSup { size 8{3} } -"17" rSup { size 8{4} } } {}

1,107,495

Got questions? Get instant answers now!

6, 053 3 size 12{6,"053" rSup { size 8{3} } } {}

This number is too big for a nonscientific calculator. A scientific calculator will probably give you 2 . 217747109 × 10 11 size 12{2 "." "217747109"´"10" rSup { size 8{"11"} } } {}

Got questions? Get instant answers now!

Exercises

For the following problems, find each value. Check each result with a calculator.

2 + 3 ( 8 ) size 12{2+3 cdot \( 8 \) } {}

26

Got questions? Get instant answers now!

18 + 7 ( 4 1 ) size 12{"18"+7 cdot \( 4-1 \) } {}

Got questions? Get instant answers now!

3 + 8 ( 6 2 ) + 11 size 12{3+8 cdot \( 6-2 \) +"11"} {}

46

Got questions? Get instant answers now!

1 5 ( 8 8 ) size 12{1-5 cdot \( 8-8 \) } {}

Got questions? Get instant answers now!

37 1 6 2 size 12{"37"-1 cdot 6 rSup { size 8{2} } } {}

1

Got questions? Get instant answers now!

98 ÷ 2 ÷ 7 2 size 12{"98"÷2÷7 rSup { size 8{2} } } {}

Got questions? Get instant answers now!

( 4 2 2 4 ) 2 3 size 12{ \( 4 rSup { size 8{2} } -2 cdot 4 \) -2 rSup { size 8{3} } } {}

0

Got questions? Get instant answers now!

9 + 14 size 12{ sqrt {9} +"14"} {}

Got questions? Get instant answers now!

100 + 81 4 2 size 12{ sqrt {"100"} + sqrt {"81"} -4 rSup { size 8{2} } } {}

3

Got questions? Get instant answers now!

8 3 + 8 2 5 size 12{ nroot { size 8{3} } {8} +8-2 cdot 5} {}

Got questions? Get instant answers now!

16 4 1 + 5 2 size 12{ nroot { size 8{4} } {"16"} -1+5 rSup { size 8{2} } } {}

26

Got questions? Get instant answers now!

61 22 + 4 [ 3 ( 10 ) + 11 ] size 12{"61"-"22"+4 \[ 3 cdot \( "10" \) +"11" \] } {}

Got questions? Get instant answers now!

121 4 [ ( 4 ) ( 5 ) 12 ] + 16 2 size 12{"121"-4 cdot \[ \( 4 \) cdot \( 5 \) -"12" \] + { {"16"} over {2} } } {}

97

Got questions? Get instant answers now!

( 1 + 16 ) 3 7 + 5 ( 12 ) size 12{ { { \( 1+"16" \) -3} over {7} } +5 cdot \( "12" \) } {}

Got questions? Get instant answers now!

8 ( 6 + 20 ) 8 + 3 ( 6 + 16 ) 22 size 12{ { {8 cdot \( 6+"20" \) } over {8} } + { {3 cdot \( 6+"16" \) } over {"22"} } } {}

29

Got questions? Get instant answers now!

10 [ 8 + 2 ( 6 + 7 ) ] size 12{"10" cdot \[ 8+2 cdot \( 6+7 \) \] } {}

Got questions? Get instant answers now!

21 ÷ 7 ÷ 3 size 12{"21"÷7÷3} {}

1

Got questions? Get instant answers now!

10 2 3 ÷ 5 2 3 2 3 size 12{"10" rSup { size 8{2} } cdot 3÷5 rSup { size 8{2} } cdot 3-2 cdot 3} {}

Got questions? Get instant answers now!

85 ÷ 5 5 85 size 12{"85"÷5 cdot 5-"85"} {}

0

Got questions? Get instant answers now!

51 17 + 7 2 5 12 3 size 12{ { {"51"} over {"17"} } +7-2 cdot 5 cdot left ( { {"12"} over {3} } right )} {}

Got questions? Get instant answers now!

2 2 3 + 2 3 ( 6 2 ) ( 3 + 17 ) + 11 ( 6 ) size 12{2 rSup { size 8{2} } cdot 3+2 rSup { size 8{3} } cdot \( 6-2 \) - \( 3+"17" \) +"11" \( 6 \) } {}

90

Got questions? Get instant answers now!

26 2 6 + 20 13 size 12{"26"-2 cdot left lbrace { {6+"20"} over {"13"} } right rbrace } {}

Got questions? Get instant answers now!

2 { ( 7 + 7 ) + 6 [ 4 ( 8 + 2 ) ] } size 12{2 cdot lbrace \( 7+7 \) +6 cdot \[ 4 cdot \( 8+2 \) \] rbrace } {}

508

Got questions? Get instant answers now!

0 + 10 ( 0 ) + 15 { 4 3 + 1 } size 12{0+"10" \( 0 \) +"15" cdot lbrace 4 cdot 3+1 rbrace } {}

Got questions? Get instant answers now!

18 + 7 + 2 9 size 12{"18"+ { {7+2} over {9} } } {}

19

Got questions? Get instant answers now!

( 4 + 7 ) ( 8 3 ) size 12{ \( 4+7 \) cdot \( 8 - 3 \) } {}

Got questions? Get instant answers now!

( 6 + 8 ) ( 5 + 2 4 ) size 12{ \( 6+8 \) cdot \( 5+2 - 4 \) } {}

144

Got questions? Get instant answers now!

( 21 3 ) ( 6 1 ) ( 7 ) + 4 ( 6 + 3 ) size 12{ \( "21" - 3 \) cdot \( 6 - 1 \) cdot \( 7 \) +4 \( 6+3 \) } {}

Got questions? Get instant answers now!

( 10 + 5 ) ( 10 + 5 ) 4 ( 60 4 ) size 12{ \( "10"+5 \) cdot \( "10"+5 \) - 4 cdot \( "60" - 4 \) } {}

1

Got questions? Get instant answers now!

6 2 8 + 3 ( 5 ) ( 2 ) + 8 4 + ( 1 + 8 ) ( 1 + 11 ) size 12{6 cdot left lbrace 2 cdot 8+3 right rbrace - \( 5 \) cdot \( 2 \) + { {8} over {4} } + \( 1+8 \) cdot \( 1+"11" \) } {}

Got questions? Get instant answers now!

2 5 + 3 ( 8 + 1 ) size 12{2 rSup { size 8{5} } +3 cdot \( 8+1 \) } {}

52

Got questions? Get instant answers now!

3 4 + 2 4 ( 1 + 5 ) size 12{3 rSup { size 8{4} } +2 rSup { size 8{4} } cdot \( 1+5 \) } {}

Got questions? Get instant answers now!

1 6 + 0 8 + 5 2 ( 2 + 8 ) 3 size 12{1 rSup { size 8{6} } +0 rSup { size 8{8} } +5 rSup { size 8{2} } cdot \( 2+8 \) rSup { size 8{3} } } {}

25,001

Got questions? Get instant answers now!

( 7 ) ( 16 ) 3 4 + 2 2 ( 1 7 + 3 2 ) size 12{ \( 7 \) cdot \( "16" \) - 3 rSup { size 8{4} } +2 rSup { size 8{2} } cdot \( 1 rSup { size 8{7} } +3 rSup { size 8{2} } \) } {}

Got questions? Get instant answers now!

2 3 7 5 2 size 12{ { {2 rSup { size 8{3} } - 7} over {5 rSup { size 8{2} } } } } {}

1 25 size 12{ { {1} over {"25"} } } {}

Got questions? Get instant answers now!

1 + 6 2 + 2 3 6 + 1 size 12{ { { left (1+6 right ) rSup { size 8{2} } +2} over {3 cdot 6+1} } } {}

Got questions? Get instant answers now!

6 2 1 2 3 3 + 4 3 + 2 3 2 5 size 12{ { {6 rSup { size 8{2} } - 1} over {2 rSup { size 8{3} } - 3} } + { {4 rSup { size 8{3} } +2 cdot 3} over {2 cdot 5} } } {}

14

Got questions? Get instant answers now!

5 8 2 9 6 2 5 7 + 7 2 4 2 2 4 5 size 12{ { {5 left (8 rSup { size 8{2} } - 9 cdot 6 right )} over {2 rSup { size 8{5} } - 7} } + { {7 rSup { size 8{2} } - 4 rSup { size 8{2} } } over {2 rSup { size 8{4} } - 5} } } {}

Got questions? Get instant answers now!

( 2 + 1 ) 3 + 2 3 + 1 10 6 2 15 2 2 5 2 5 5 2 size 12{ { { \( 2+1 \) rSup { size 8{3} } +2 rSup { size 8{3} } +1 rSup { size 8{"10"} } } over {6 rSup { size 8{2} } } } - { {"15" rSup { size 8{2} } - left [2 cdot 5 right ] rSup { size 8{2} } } over {2 rSup { size 8{4} } - 5} } } {}

0

Got questions? Get instant answers now!

6 3 2 10 2 2 2 + 18 ( 2 3 + 7 2 ) 2 ( 19 ) 3 3 size 12{ { {6 rSup { size 8{3} } - 2 cdot "10" rSup { size 8{2} } } over {2 rSup { size 8{2} } } } + { {"18" \( 2 rSup { size 8{3} } +7 rSup { size 8{2} } \) } over {2 \( "19" \) - 3 rSup { size 8{3} } } } } {}

Got questions? Get instant answers now!

2 6 + 10 2 6 25 size 12{2 cdot left lbrace 6+ left ["10" rSup { size 8{2} } - 6 sqrt {"25"} right ] right rbrace } {}

152

Got questions? Get instant answers now!

181 3 2 36 + 3 64 3 size 12{"181" - 3 cdot left (2 sqrt {"36"} +3 nroot { size 8{3} } {"64"} right )} {}

Got questions? Get instant answers now!

2 81 125 3 4 2 10 + 2 2 size 12{ { {2 cdot left ( sqrt {"81"} - nroot { size 8{3} } {"125"} right )} over {4 rSup { size 8{2} } - "10"+2 rSup { size 8{2} } } } } {}

4 5 size 12{ { {4} over {5} } } {}

Got questions? Get instant answers now!

Exercises for review

( [link] ) The fact that 0 + any whole number = that particular whole number is an example of which property of addition?

Got questions? Get instant answers now!

( [link] ) Find the product. 4, 271 × 630 size 12{4,"271" times "630"} {} .

2,690,730

Got questions? Get instant answers now!

( [link] ) In the statement 27 ÷ 3 = 9 size 12{"27" div 3=9} {} , what name is given to the result 9?

Got questions? Get instant answers now!

( [link] ) What number is the multiplicative identity?

1

Got questions? Get instant answers now!

( [link] ) Find the value of 2 4 size 12{2 rSup { size 8{4} } } {} .

Got questions? Get instant answers now!

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min
Tanis Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask