8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4....
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Transcript of 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4....
![Page 1: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/1.jpg)
8.2 P.O.D. Simplify the following expressions.
1. 2(y2)5
2. 3x3 + 2x3
3. (2x)(4x2)(-10x3)
4. 3(x3)5
5. -3x2 + x4
![Page 2: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/2.jpg)
Quotients of Powers
Section 8.3
![Page 3: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/3.jpg)
Big Idea
• Because of the relationship between multiplication and division, quotients of powers can be themselves written as powers
Goal• Develop and apply the Quotient of Powers
Property
![Page 4: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/4.jpg)
HW Answers 8.2
![Page 5: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/5.jpg)
Quotient of Powers
• By expanding the exponent and cross cancelling you can simplify division of powers.
• EX:
• Can you think of a short cut to get the same result?
53
2
x x x x x xx x x x
x x x
![Page 6: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/6.jpg)
Quotient of Powers Rule: for all non zero b, if you divide two powers with the same bases, you can subtract the exponents.
mm n
n
bb
b
![Page 7: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/7.jpg)
REMEMBER – Coefficients still need to be divided not SUBTRACTED
125 5
7
2015 4
5
xx x
x
![Page 8: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/8.jpg)
1) Change the following to a simplified power:
a. b.
c.
12
3
4
43
12 9
4 1
4 4
13
13
5
5
412-3 = 49 43-12 = 4-9
513-13 = 50 = 1
8.3
![Page 9: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/9.jpg)
2) In March, 1992, there was a total of 283.9 billion dollars in U.S. currency in circulation. The U.S. population was about 252.7 million. how much currency per person was in circulation?
11 11
8 8
283,900,000,000 2.839 10 2.839 10
252,700,000 2.527 10 2.527 10
≈ 1.12347 x 103 ≈ $1,123.47 per person
8.3
![Page 10: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/10.jpg)
3) Simplify
a) b)
c) d)
2 10
15
30
25
x y
xy
7
2
12
3
x
x
14
17
28x10
7x10
5
8
a
a
5
6
5
x
y = 4x5
4·10-3=
1 441000 1000
.004
3
1
a
8.3
![Page 11: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/11.jpg)
Quiz Review: 8-1 through 8-3
1) Fill in the blank with properties of exponents(includes the Quotient of a powers property)
a) bm ∙ bn = b) (bm)n = c) = bm-n d) 49500000 = scientific notation
e) 4.394 x 10-6 =
bm+n bm·n
bm/bn 4.95 x 107
0.000004394
Rev1
![Page 12: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/12.jpg)
2) Simplify an expression.
4 5 1 3
2 4 2 3
56 4
16 7
x y xz x y z
xy z x z
Simplify coefficients, use properties
= 2x4-3y-7+3z5+4 = 2xy-4z9 =
Cancel coefficients, use properties
7
2x4+1-1y-5-2z1-(-4)
4
7x-1-2y3z1-(-3)=
Rev1
9
4
2xz
y
Simplified expressions have no negative exponents
![Page 13: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/13.jpg)
A lot of examples to try:10
6
8
6
6
10
6
1.
2.
3.
504.5
x
x
x
x
x
x
x
x
14
7
2
6 7
2 5
9
9
145.7
306.
5
47.2
188.6
x
x
x
x
x y
x y
x
x
14
7
2
2
5 9
2 2
9
3
39.19
3010.
5
1611.32
1812.
6
x
y
x
x
x y
x y z
x
y
![Page 14: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/14.jpg)
Practice
10
6
(4 )
(4 )
x
x
4(4 )x
![Page 15: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/15.jpg)
Practice
2 3 4( 9 )( 4 )x y x y
6 436x y
![Page 16: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/16.jpg)
Practice
2 4(2 )( 4 )(4 )x x y y
6 232x y
![Page 17: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/17.jpg)
Practice
12 40 23(2 )( 4 )(4 )x x y
758x
![Page 18: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/18.jpg)
Practice
(3 )x y
3xy
![Page 19: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/19.jpg)
Practice
11
8
x
x
3x
![Page 20: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/20.jpg)
Practice
8
yx
x
8yx
![Page 21: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/21.jpg)
Practice
9
11
a
b
9
11
a
b
![Page 22: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/22.jpg)
Practice
9 13
2 11
x y
x y
7 2x y
![Page 23: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/23.jpg)
Practice
8
7
20
4
y
y
5y
![Page 24: 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4.](https://reader036.fdocuments.us/reader036/viewer/2022062314/56649f2b5503460f94c46076/html5/thumbnails/24.jpg)
Practice
1022
2
y
y
911y