WARM UP 3 SIMPLIFY THE EXPRESSION ● (2 3 ) 2

WARM UP 2 SIMPLIFY THE EXPRESSION ● (2 3 ) 2

WARM UP 1 SIMPLIFY THE EXPRESSION ● (2 3 ) 2

WARM UP 0 SIMPLIFY THE EXPRESSION ● (2 3 ) 2

8.1 Multiplication Properties of Exponents EXPONENTIAL TERMS xyxy base exponent

8.1 Multiplication Properties of Exponents A base raised to an exponent means the base multiplied by itself to the number of copies represented by the exponent. x4x4 =x·x·x·x

8.1 Multiplication Properties of Exponents PRODUCT OF POWERS To multiply powers that have the same base, you ADD the exponents. This property is called the Product of Powers Property. a 2 · a 3 = a · a · a · a · a = a 5 (a 2+3 )

8.1 Multiplication Properties of Exponents POWER OF A POWER To find a power of a power, you multiply the exponents. This property is called the Power of a Power Property. (a 2 ) 3 = a 2 · a 2 · a 2 = a =a 6

8.1 Multiplication Properties of Exponents POWER OF A PRODUCT To find the power of a product, find the power of each factor and multiply. This property is called the Power of a Product Property. (a · b) 3 = (a · b) (a · b) (a · b) = (a·a·a)(b·b·b) =a 3 b 3

8.1 Multiplication Properties of Exponents Simplify the expression. a) (-6x) 3 b) (4yz) 3 c) (2x) 3 d) (-3x) 2 e) (2w) 6 f) (7a) 2

8.1 Multiplication Properties of Exponents Use All Three Properties Simplify the expression (4x 2 ) 3 · x 5 SOLUTION Use power of a product property Use power of a power property Use product of powers property

8.1 Multiplication Properties of Exponents Use All Three Properties Simplify the expression (4x 3 ) 4 (-3a 4 ) 2 (9z 5 ) 2 · 9 (x 2 ) 3 · x 7

8.1 Multiplication Properties of Exponents SUMMARY Multiplication Properties of Exponents PRODUCT OF POWERS PROPERTY a m · a n = a m+n POWER OF A POWER PROPERTY (a m ) n = a mn POWER OF A PRODUCT PROPERTY (a · b) m = a m b m

8.1 Multiplication Properties of Exponents YOUR TURN Textbook pages 446 and 447 #s and 52-60