thinking mathematically number theory and the real number system 5.6 exponents and scientific...
TRANSCRIPT
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
?
2
2
?2
?44
4
8
32
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,
Example:4-2 = 1/42 = 1/16
5-3 = 1/53 = 1/125
7-1 = 1/71 = 1/7
mm
bb
1
Exercise Set 5.6 #19
2-2 = ?
Properties of Exponents
Example• Exercise Set 5.6 #27
333
Thinking Mathematically
Number Theory and the Real Number System
5.6 Exponents and Scientific Notation