Section P2
Exponents and Scientific Notation
The Product Rule
Example
Simplify:
 7 x  9 x 
5
3
3
5 2
5
x
y
4
x
  y 
The Quotient Rule
Example
Simplify:
 2 
3
 2 
7
4
8 x y3
2 x
Example
Simplify:
48 x5 y 3 z 2
2
16 x y
Zero as an Exponent
Example
Simplify:
5
0
7
7
6 z
5
6
x x
The Negative-Exponent Rule
Example
(5)
5
2
2
2
3x y
4
Simplify Exponential
Expressions
Example
4
4
1
2
7
Simplify Exponential
Expressions
The Power Rule for Exponents
(Powers to Powers)
Example
b 
 3 
y 
5
4
2
4
Simplify Exponential
Expressions
5
2
Power of a Product
Example
Simplify Exponential
Expressions
 3x 
4 3
 6x y 
3
2
Power of a Quotient
Example
x 
 3
y 
4
Simplify Exponential
Expressions
2
 5x 
 3 
 y 
2
3
Simplifying Exponential
Expressions
Example
Simplify Exponential
Expressions
( 2 x 3 y ) 4
2 8
3 8

7
x
y

2
x

 y 
4 x y
5 4
2x y
3
7
 54 yz 

2 
 6z 
7
2
Use Scientific Notation
Converting from Scientific to Decimal Notation
In a × 10n 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.
Example
8.3  10
Convert from Scientific Notation to
decimal notation.
5
2.09  10
4
4.045  10
2
Example
Convert from decimal notation to
scientific notation.
56,000,000
4,090,000
0.0000067
0.00000.36
Example
Perform the indicated operations and write your
answer in scientific notation.
 7.3 10 8.0 10 
6
4.8  10
3
3.0  10
7
8
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
2 3
 3xy 
(a) 27 x 3 y 6
(b) 27 x 3 y 6
(c) 9 xy 6
(d) 9 x 3 y 6
Simplify the exponential expression
 30 x y 

2 4 
 15 x y 
5
(a)
4 x 6 y14
(b)
4 x6 y 7
(c)
4 x 6 y14
(d)
2 x 3 y 7
3
2
Perform the indicated operation and write your
answer in scientific notation.
4,640,000,000
232,000
(a) .2 103
(b) 2 1014
(c) 2 104
(d) 2 1045