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. b m b n =b m+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. (b n ) m = b nm The Quotient Rule: Subtract exponents when dividing with the same base.Use this difference as the exponent of the common base. b m /b n = b m - n

Examples: Properties of Exponents Exercise Set 5.6 #3, 5, 11 Use the properties of exponents to simplify, then evaluate

The Zero Exponent Rule If b is any real number other than 0. b 0 = 1 Example: 7 0 = 1 π 0 = 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 = 1/4 2 = 1/ = 1/5 3 = 1/ = 1/7 1 = 1/7 Exercise Set 5.6 # = ?

Properties of Exponents Example Exercise Set 5.6 #27

Thinking Mathematically Number Theory and the Real Number System 5.6 Exponents and Scientific Notation