Int Math 2 Section 2-7/2-8 1011
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Transcript of Int Math 2 Section 2-7/2-8 1011
![Page 1: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/1.jpg)
SECTIONS 2-7 AND 2-8Properties of Exponents and Zero and Negative
Exponents
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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
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VOCABULARY
1. Exponential Form:
2. Base:
3. Exponent:4. Standard Form:5. Scientific Notation:
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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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/9.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 10: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/10.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 11: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/11.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 12: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/12.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 13: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/13.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 14: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/14.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern:
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 15: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/15.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 16: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/16.jpg)
ORGANISM ACTIVITY
Hours 1 2 3 4 5
# of organisms
2 4 8 16 32
Pattern: The number of organisms doubles
Sixth hour: 64 Seventh hour: Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 17: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/17.jpg)
ORGANISM ACTIVITY
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 Tenth hour:
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 18: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/18.jpg)
ORGANISM ACTIVITY
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 Tenth hour: 1024
How long until there are 2000?
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 19: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/19.jpg)
ORGANISM ACTIVITY
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 Tenth hour: 1024
How long until there are 2000? 11th hour
An organism divides into two new organisms each hour. Fill in the table for the number of organisms after each hour.
![Page 20: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/20.jpg)
EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
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EXAMPLE 1
Evaluate for x = .8 and y = 1.2.
a. 3x2 y b. (4x)3 y2
3(.8)2(1.2)
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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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/28.jpg)
PRODUCT RULE
bmibn = bm+n
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PRODUCT RULE
bmibn = bm+n
x3 ix5 =
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PRODUCT RULE
bmibn = bm+n
x3 ix5 = xixix
![Page 31: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/31.jpg)
PRODUCT RULE
bmibn = bm+n
x3 ix5 = xixix ixixixixix
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PRODUCT RULE
bmibn = bm+n
x3 ix5 = xixix ixixixixix = x8
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POWER RULE
(bm )n = bmn
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POWER RULE
(bm )n = bmn
(y2 )3
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POWER RULE
(bm )n = bmn
(y2 )3 = y2 iy2 iy2
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POWER RULE
(bm )n = bmn
(y2 )3 = y2 iy2 iy2
= y6
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POWER OF A PRODUCT RULE
(ab)m = ambm
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POWER OF A PRODUCT RULE
(ab)m = ambm
(gf )4
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POWER OF A PRODUCT RULE
(ab)m = ambm
(gf )4 = gf igf igf igf
![Page 40: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/40.jpg)
POWER OF A PRODUCT RULE
(ab)m = ambm
(gf )4 = gf igf igf igf = g4 f 4
![Page 41: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/41.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
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QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3
![Page 43: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/43.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 44: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/44.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 45: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/45.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 46: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/46.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic
![Page 47: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/47.jpg)
QUOTIENT RULE
bm ÷ bn =
bm
bn = bm−n
c5
c3 =
ciciciciccicic = c2
![Page 48: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/48.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
![Page 49: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/49.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
dw
⎛⎝⎜
⎞⎠⎟
3
![Page 50: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/50.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
dw
⎛⎝⎜
⎞⎠⎟
3
=
dw
idw
idw
![Page 51: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/51.jpg)
POWER OF A QUOTIENT RULE
ab
⎛⎝⎜
⎞⎠⎟
m
=am
bm
dw
⎛⎝⎜
⎞⎠⎟
3
=
dw
idw
idw
=d3
w3
![Page 52: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/52.jpg)
EXAMPLE 2
Simplify.
a. 32 i35 b. (6m4 )2
![Page 53: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/53.jpg)
EXAMPLE 2
Simplify.
a. 32 i35 b. (6m4 )2
32+5
![Page 54: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/54.jpg)
EXAMPLE 2
Simplify.
a. 32 i35 b. (6m4 )2
32+5
37
![Page 55: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/55.jpg)
EXAMPLE 2
Simplify.
a. 32 i35 b. (6m4 )2
32+5
37
2187
![Page 56: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/56.jpg)
EXAMPLE 2
Simplify.
a. 32 i35 b. (6m4 )2
32+5
37
2187
62 m4(2)
![Page 57: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/57.jpg)
EXAMPLE 2
Simplify.
a. 32 i35 b. (6m4 )2
32+5
37
2187
62 m4(2)
36m8
![Page 58: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/58.jpg)
EXAMPLE 3
Evaluate for x = 1/2 and y = 2/3.
a. x2 y b. 3x3 y2
![Page 59: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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
312( )3 2
3( )2
![Page 64: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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
312( )3 2
3( )2
318( ) 4
9( )
![Page 65: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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
312( )3 2
3( )2
318( ) 4
9( ) 3
472( )
![Page 66: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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
312( )3 2
3( )2
318( ) 4
9( ) 3
472( )
1272
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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
312( )3 2
3( )2
318( ) 4
9( ) 3
472( )
1272
16
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ZERO PROPERTY OF EXPONENTS
b0 = 1
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ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4
![Page 70: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/70.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4
![Page 71: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/71.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4 = x0
![Page 72: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/72.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4 = x0
x4
x4
![Page 73: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/73.jpg)
ZERO PROPERTY OF EXPONENTS
b0 = 1
x4
x4 = x4−4 = x0
x4
x4 = 1
![Page 74: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/74.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
![Page 75: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/75.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7
![Page 76: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/76.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7
![Page 77: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/77.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
![Page 78: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/78.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
h3
h7
![Page 79: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/79.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
h3
h7 =
hihihhihihihihihih
![Page 80: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/80.jpg)
PROPERTY OF NEGATIVE EXPONENTS
b−m
=
1bm
h3
h7 = h3−7 = h−4
h3
h7 =
hihihhihihihihihih
=1h4
![Page 81: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/81.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
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EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
![Page 83: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/83.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
![Page 84: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/84.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
1x6
![Page 85: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/85.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
1x6
y3
y4
![Page 86: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/86.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
1x6
y3
y4
y−1
![Page 87: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/87.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
1x6
y3
y4
y−1
1y
![Page 88: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/88.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
1x6
y3
y4
y−1
1y
z−6
![Page 89: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/89.jpg)
EXAMPLE 4
Simplify each expression. Write the answer with a positive exponent.
a. x2
x8
b. y3 i
1y4 c. (z−3 )2
x2−8
x−6
1x6
y3
y4
y−1
1y
z−6
1z6
![Page 90: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/102.jpg)
EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
![Page 103: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/103.jpg)
EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
1.3i10-6
![Page 104: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/104.jpg)
EXAMPLE 6
Write in scientific notation.
a. .0000013 b. 230,000,000,000
1.3i10-6 2.3i1011
![Page 105: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/105.jpg)
EXAMPLE 7
Write in standard form.
a. 7.2i106 b. 3.5i10−9
![Page 106: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/106.jpg)
EXAMPLE 7
Write in standard form.
a. 7.2i106 b. 3.5i10−9
7, 200,000
![Page 107: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/107.jpg)
EXAMPLE 7
Write in standard form.
a. 7.2i106 b. 3.5i10−9
7, 200,000 .0000000035
![Page 108: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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)(1015 i10−24 )
![Page 111: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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)(1015 i10−24 )
4.509i10−9
![Page 112: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/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)(1015 i10−24 )
4.509i10−9
.000000004509 gram
![Page 113: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/113.jpg)
PROBLEM SET
![Page 114: Int Math 2 Section 2-7/2-8 1011](https://reader035.fdocuments.in/reader035/viewer/2022062419/558ce70ad8b42aab628b4792/html5/thumbnails/114.jpg)
PROBLEM SET
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