Transcript Thinking Mathematically by Robert Blitzer

Thinking
Mathematically
Number Theory and the Real Number
System
5.6 Exponents and Scientific Notation
Properties of Exponents
The Product Rule: Add exponents when
multiplying with the same base. Use the sum as
the exponent of the common base. bmbn = bm+n
The Power Rule: Multiply exponents when an
exponential expression is raised to a power. Place
the product of the exponents on the base and
remove the parentheses. (bn)m = bnm
The Quotient Rule: Subtract exponents when
dividing with the same base. Use this difference
as the exponent of the common base. bm/bn = bm - n
Examples: Properties of Exponents
Exercise Set 5.6 #3, 5, 11
Use the properties of exponents to simplify, then evaluate
44  ?
2
2 
2 3
8
?
2
?
4
2
The Zero Exponent Rule
If b is any real number other than 0.
b0 = 1
Example:
70 = 1
π0 = 1
(-5)0 = 1
The Negative Exponent Rule
If b is any real number other than 0, and
m is a natural number,
b
Example:
4-2 = 1/42 = 1/16
5-3 = 1/53 = 1/125
7-1 = 1/71 = 1/7
Exercise Set 5.6 #19
2-2 = ?
m
1
 m
b
Properties of Exponents
Example
• Exercise Set 5.6 #27
3 3 
3
Thinking
Mathematically
Number Theory and the Real Number
System
5.6 Exponents and Scientific Notation