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