0.2 bzca5e
Transcript of 0.2 bzca5e
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Section P2Exponents and Scientific Notation
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The Product Rule
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Example
3 5 25 4x y x y
Simplify:
5 37 9x x
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The Quotient Rule
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Example
7
3
2
2
Simplify:
48 3
2
x y
x
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Example
5 3 2
2
48
16
x y z
x y
Simplify:
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Zero as an Exponent
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Example
5 0
5
6
6
z
7 7x x
Simplify:
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The Negative-Exponent Rule
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Example
2( 5)
2 43x y
Simplify Exponential Expressions
25
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Example
44
2
1
7
Simplify Exponential Expressions
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The Power Rule for Exponents
(Powers to Powers)
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Example
45
22
54
3
b
y
Simplify Exponential Expressions
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Power of a Product
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Example
343x
236x y
Simplify Exponential Expressions
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Power of a Quotient
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Example
32
3
5x
y
24
3
x
y
Simplify Exponential Expressions
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Simplifying Exponential Expressions
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Example
3 4
2 8 3 8
3 7
5 4
27
2
( 2 )
7 2
4
2
54
6
x y
x y x y
x y
x y
yz
z
Simplify Exponential Expressions
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Use Scientific Notation
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nIn a × 10 change a number in scientific notation
to decimal notation by moving the decimal point in
a to the right if n is positive, and move the decimal
point to the left if n is negative, n number of places.
Converting from Scientific to Decimal Notation
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Example Convert from Scientific Notation to decimal notation.
5
4
2
8.3 10
2.09 10
4.045 10
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Example Convert from decimal notation to scientific notation.
56,000,000
4,090,000
0.0000067
0.00000.36
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Example
6 8
7
3
7.3 10 8.0 10
4.8 10
3.0 10
Perform the indicated operations and write your answer in scientific notation.
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Example
In 2008, Congress proposed a 700 billion dollar bailout (7 x 1011) of the US banking system. If there are 300 million people in the US, what will be the cost per person in tax dollars if every person paid an equal amount of this bailout cost?
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Simplify the exponential expression
(a)
(b)
(c)
(d)
323xy
3 6
3 6
6
3 6
27
27
9
9
x y
x y
xy
x y
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Simplify the exponential expression
(a)
(b)
(c)
(d)
25 3
2 4
30
15
x y
x y
6 14
6 7
6 14
3 7
4
4
4
2
x y
x y
x y
x y
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Perform the indicated operation and write your answer in scientific notation.
(a)
(b)
(c)
(d)
4,640,000,000
232,000
3
14
4
45
.2 10
2 10
2 10
2 10