integrated math 2 sections 2-7 and 2-8
DESCRIPTION
Properties of Exponents and Zero and Negative ExponentsTRANSCRIPT
![Page 1: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/1.jpg)
SECTIONS 2-7 AND 2-8Properties of Exponents and Zero and Negative
Exponents
![Page 2: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/2.jpg)
ESSENTIAL QUESTIONS
How do you choose appropriate units of measure?
How do you evaluate variable expressions?
How do you write numbers using zero and negative integers as exponents?
How do you write numbers in scientific notation?
Where you’ll see this:
Biology, finance, computers, population, physics, astronomy
![Page 3: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/3.jpg)
VOCABULARY
1. Exponential Form:
2. Base:
3. Exponent:4. Standard Form:5. Scientific Notation:
![Page 4: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/4.jpg)
VOCABULARY
1. Exponential Form: The form you use to represent multiplying a number by itself numerous times
2. Base:
3. Exponent:4. Standard Form:5. Scientific Notation:
![Page 5: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/5.jpg)
VOCABULARY
1. Exponential Form: The form you use to represent multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and over
3. Exponent:4. Standard Form:5. Scientific Notation:
![Page 6: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/6.jpg)
VOCABULARY
1. Exponential Form: The form you use to represent multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and over
3. Exponent: The number of times we multiply the base4. Standard Form:5. Scientific Notation:
![Page 7: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/7.jpg)
VOCABULARY
1. Exponential Form: The form you use to represent multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and over
3. Exponent: The number of times we multiply the base4. Standard Form: Any number in decimal form5. Scientific Notation:
![Page 8: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/8.jpg)
VOCABULARY
1. Exponential Form: The form you use to represent multiplying a number by itself numerous times
2. Base: The number that is being multiplied over and over
3. Exponent: The number of times we multiply the base4. Standard Form: Any number in decimal form5. Scientific Notation: A number with two factors, where
the first factor is a number ≥ 1 and < 10, and the second is a power of 10.
![Page 9: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/9.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 10: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/10.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 11: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/11.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 12: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/12.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 13: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/13.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 14: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/14.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 15: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/15.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: Seventh hour: Eighth hour:
How long until there are 2000?
![Page 16: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/16.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: Eighth hour:
How long until there are 2000?
![Page 17: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/17.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: 128 Eighth hour:
How long until there are 2000?
![Page 18: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/18.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: 128 Eighth hour: 256
How long until there are 2000?
![Page 19: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/19.jpg)
ACTIVITY: PAGE 82
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: 128 Eighth hour: 256
How long until there are 2000? 11th hour
![Page 20: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/20.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
![Page 21: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/21.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
![Page 22: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/22.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
= 3(.64)(1.2)
![Page 23: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/23.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
= 3(.64)(1.2)
= 2.304
![Page 24: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/24.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
= 3(.64)(1.2)
= 2.304
= [4(.8)]3(1.2)2
![Page 25: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/25.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
= 3(.64)(1.2)
= 2.304
= [4(.8)]3(1.2)2
= (3.2)3(1.2)2
![Page 26: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/26.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
= 3(.64)(1.2)
= 2.304
= [4(.8)]3(1.2)2
= (3.2)3(1.2)2
= (32.768)(1.44)
![Page 27: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/27.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
= 3(.8)2(1.2)
= 3(.64)(1.2)
= 2.304
= [4(.8)]3(1.2)2
= (3.2)3(1.2)2
= (32.768)(1.44)
= 47.18592
![Page 28: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/28.jpg)
PRODUCT RULE
bmibn = bm+n
![Page 29: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/29.jpg)
PRODUCT RULE
bmibn = bm+n
x3ix5 =
![Page 30: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/30.jpg)
PRODUCT RULE
bmibn = bm+n
x3ix5 = xixix
![Page 31: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/31.jpg)
PRODUCT RULE
bmibn = bm+n
x3ix5 = xixix ixixixixix
![Page 32: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/32.jpg)
PRODUCT RULE
bmibn = bm+n
x3ix5 = xixix ixixixixix = x8
![Page 33: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/33.jpg)
POWER RULE
(bm )n = bmn
![Page 34: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/34.jpg)
POWER RULE
(bm )n = bmn
(y2 )3
![Page 35: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/35.jpg)
POWER RULE
(bm )n = bmn
(y2 )3 = y2
iy2iy2
![Page 36: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/36.jpg)
POWER RULE
(bm )n = bmn
(y2 )3 = y2
iy2iy2
= y6
![Page 37: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/37.jpg)
POWER OF A PRODUCT RULE
(ab)m = ambm
![Page 38: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/38.jpg)
POWER OF A PRODUCT RULE
(ab)m = ambm
(gf )4
![Page 39: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/39.jpg)
POWER OF A PRODUCT RULE
(ab)m = ambm
(gf )4 = gf igf igf igf
![Page 40: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/40.jpg)
POWER OF A PRODUCT RULE
(ab)m = ambm
(gf )4 = gf igf igf igf = g4 f 4
![Page 41: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/41.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
![Page 42: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/42.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3
![Page 43: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/43.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 44: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/44.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 45: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/45.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 46: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/46.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 47: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/47.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic = c2
![Page 48: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/48.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
![Page 49: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/49.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
dw
⎛⎝⎜
⎞⎠⎟
3
![Page 50: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/50.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
dw
⎛⎝⎜
⎞⎠⎟
3
=
dw
idw
idw
![Page 51: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/51.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
dw
⎛⎝⎜
⎞⎠⎟
3
=
dw
idw
idw
=d3
w3
![Page 52: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/52.jpg)
EXAMPLE 2
Simplify.
a. 32i35
b. (6m4 )2
![Page 53: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/53.jpg)
EXAMPLE 2
Simplify.
a. 32i35
b. (6m4 )2
= 32+5
![Page 54: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/54.jpg)
EXAMPLE 2
Simplify.
a. 32i35
b. (6m4 )2
= 32+5
= 37
![Page 55: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/55.jpg)
EXAMPLE 2
Simplify.
a. 32i35
b. (6m4 )2
= 32+5
= 37
= 2187
![Page 56: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/56.jpg)
EXAMPLE 2
Simplify.
a. 32i35
b. (6m4 )2
= 32+5
= 37
= 2187
= 62 m4(2)
![Page 57: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/57.jpg)
EXAMPLE 2
Simplify.
a. 32i35
b. (6m4 )2
= 32+5
= 37
= 2187
= 62 m4(2)
= 36m8
![Page 58: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/58.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
![Page 59: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/59.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( )
![Page 60: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/60.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( )
![Page 61: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/61.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
![Page 62: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/62.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
=16
![Page 63: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/63.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
=16
= 3 12( )3 2
3( )2
![Page 64: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/64.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
=16
= 3 12( )3 2
3( )2
= 3 18( ) 4
9( )
![Page 65: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/65.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
=16
= 3 12( )3 2
3( )2
= 3 18( ) 4
9( ) = 3 4
72( )
![Page 66: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/66.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
=16
= 3 12( )3 2
3( )2
= 3 18( ) 4
9( ) = 3 4
72( )
=1272
![Page 67: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/67.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
=12( )2 2
3( ) =
14( ) 2
3( ) =
212
=16
= 3 12( )3 2
3( )2
= 3 18( ) 4
9( ) = 3 4
72( )
=1272 =
16
![Page 68: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/68.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
![Page 69: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/69.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4
![Page 70: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/70.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4
![Page 71: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/71.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4 = x0
![Page 72: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/72.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4 = x0
x4
x4
![Page 73: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/73.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4 = x0
x4
x4 = 1
![Page 74: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/74.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
![Page 75: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/75.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7
![Page 76: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/76.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7
![Page 77: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/77.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
![Page 78: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/78.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
h3
h7
![Page 79: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/79.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
h3
h7 =
hihihhihihihihihih
![Page 80: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/80.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
h3
h7 =
hihihhihihihihihih
=1h4
![Page 81: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/81.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
![Page 82: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/82.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
![Page 83: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/83.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
![Page 84: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/84.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
=
1x6
![Page 85: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/85.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
=
1x6
=
y3
y4
![Page 86: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/86.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
=
1x6
=
y3
y4
= y−1
![Page 87: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/87.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
=
1x6
=
y3
y4
= y−1
=
1y
![Page 88: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/88.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
=
1x6
=
y3
y4
= y−1
=
1y
= z−6
![Page 89: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/89.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3
i1y4 c. (z−3 )2
= x2−8
= x−6
=
1x6
=
y3
y4
= y−1
=
1y
= z−6
=
1z6
![Page 90: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/90.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
![Page 91: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/91.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
![Page 92: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/92.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
![Page 93: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/93.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
![Page 94: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/94.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
![Page 95: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/95.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
![Page 96: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/96.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
=
146
![Page 97: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/97.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
=
146
=1
4096
![Page 98: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/98.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
=
146
=1
4096
= (−2)5(4)−3
![Page 99: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/99.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
=
146
=1
4096
= (−2)5(4)−3
=
(−2)5
(4)3
![Page 100: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/100.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
=
146
=1
4096
= (−2)5(4)−3
=
(−2)5
(4)3
=−3264
![Page 101: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/101.jpg)
EXAMPLE 5
Evaluate each expression when m = -2 and n = 4.
a. 6m4 b. (n3 )−2 c. m5n−3
= 6(−2)4
= 6(16)
= 96
= n−6
=
1n6
=
146
=1
4096
= (−2)5(4)−3
=
(−2)5
(4)3
=−3264
=−12
![Page 102: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/102.jpg)
EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
![Page 103: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/103.jpg)
EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
=1.3i10-6
![Page 104: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/104.jpg)
EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
=1.3i10-6 =2.3i1011
![Page 105: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/105.jpg)
EXAMPLE 7
Write in standard form.
a. 7.2i106 b. 3.5i10−9
![Page 106: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/106.jpg)
EXAMPLE 7
Write in standard form.
a. 7.2i106 b. 3.5i10−9
= 7,200,000
![Page 107: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/107.jpg)
EXAMPLE 7
Write in standard form.
a. 7.2i106 b. 3.5i10−9
= 7,200,000 = .0000000035
![Page 108: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/108.jpg)
EXAMPLE 8
The mass of one hydrogen atom is 1.67i10−24
grams. Find the mass of 2,700,000,000,000,000 hydrogen atoms.
![Page 109: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/109.jpg)
EXAMPLE 8
The mass of one hydrogen atom is 1.67i10−24
grams. Find the mass of 2,700,000,000,000,000 hydrogen atoms.
(1.67i10−24 )(2.7i1015 )
![Page 110: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/110.jpg)
EXAMPLE 8
The mass of one hydrogen atom is 1.67i10−24
grams. Find the mass of 2,700,000,000,000,000 hydrogen atoms.
(1.67i10−24 )(2.7i1015 )
= (1.67i2.7)(1015i10−24 )
![Page 111: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/111.jpg)
EXAMPLE 8
The mass of one hydrogen atom is 1.67i10−24
grams. Find the mass of 2,700,000,000,000,000 hydrogen atoms.
(1.67i10−24 )(2.7i1015 )
= (1.67i2.7)(1015i10−24 )
= 4.509i10−9
![Page 112: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/112.jpg)
EXAMPLE 8
The mass of one hydrogen atom is 1.67i10−24
grams. Find the mass of 2,700,000,000,000,000 hydrogen atoms.
(1.67i10−24 )(2.7i1015 )
= (1.67i2.7)(1015i10−24 )
= 4.509i10−9
= .000000004509 gram
![Page 113: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/113.jpg)
HOMEWORK
![Page 114: Integrated Math 2 Sections 2-7 and 2-8](https://reader038.vdocuments.site/reader038/viewer/2022103116/558ce733d8b42a9c628b47b1/html5/thumbnails/114.jpg)
HOMEWORK
p. 84 #1-48 multiples of 3; p. 88 #1-48 multiples of 3
“When you’re screwing up and nobody’s saying anything to you anymore, that means they gave up [on you]...When
you see yourself doing something badly and nobody’s bothering to tell you anymore, that’s a very bad place to be. Your critics are the ones who are telling you they still
love and care.” - Randy Pausch