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Section P2Exponents and Scientific Notation
The Product Rule
Example
3 5 25 4x y x y
Simplify:
5 37 9x x
The Quotient Rule
Example
7
3
2
2
Simplify:
48 3
2
x y
x
Example
5 3 2
2
48
16
x y z
x y
Simplify:
Zero as an Exponent
Example
5 0
5
6
6
z
7 7x x
Simplify:
The Negative-Exponent Rule
Example
2( 5)
2 43x y
Simplify Exponential Expressions
25
Example
44
2
1
7
Simplify Exponential Expressions
The Power Rule for Exponents
(Powers to Powers)
Example
45
22
54
3
b
y
Simplify Exponential Expressions
Power of a Product
Example
343x
236x y
Simplify Exponential Expressions
Power of a Quotient
Example
32
3
5x
y
24
3
x
y
Simplify Exponential Expressions
Simplifying Exponential Expressions
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
Use Scientific Notation
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
Example Convert from Scientific Notation to decimal notation.
5
4
2
8.3 10
2.09 10
4.045 10
Example Convert from decimal notation to scientific notation.
56,000,000
4,090,000
0.0000067
0.00000.36
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.
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?
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
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
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
