Using Properties of Exponents

Properties of Exponents a&b are real numbers, m&n are integers Product Property: am * an=am+n Power of a Power Property: (am)n=amn Power of a Product Property: (ab)m=ambm Negative Exponent Property: a-m= ; a≠0 Zero Exponent Property: a0=1; a≠0 Quotient of Powers: am = am-n; a≠0 an Power of Quotient: b≠0

Example 1 – Product Property (-5)4 * (-5)5 = (-5)4+5 = (-5)9 = -1953125

Example 2 x5 * x2 = x5+2 = x7

Example 3 – Power of a Power (23)4 = 23*4 = 212 = 4096

Example 4 (34)2 = 34*2 = 38 = 6561

Example 5 – Neg. Exponent (-5)-6(-5)4 = (-5)-6+4 = (-5)-2 =

Example 6 – Quotient of Powers

Example 7 – Power of Quotient

Example 8 – Zero Exponent (7b-3)2 b5 b = 72 b-3*2 b5 b = 49 b-6+5+1 = 49b0 = 49

Example 9 – Quotient of Powers

How many places did you have to move the decimal? Scientific Notation 131,400,000,000= 1.314 x 1011 Put that number here! Move the decimal behind the 1st number How many places did you have to move the decimal?

Example – Scientific Notation 131,400,000,000 = 5,284,000 1.314 x 1011 = 5.284 x 106