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Properties of Exponents Product Property Power of a Power Property Power of a Product Property Quotient Property Power of a Quotient Property Zero Property Negative Exponent Property Product Property Expand the expressions and then re-combine so you can simplify the expression. Example 1: 3 3 (3 3 3)(3 3 3 3) 37 3 4 There are a total of 7 3’s. Example 2: xx 6 2 ( x x x x x x)(x x) x 8 There are a total of 8 x’s. Product Property Expand the expressions and then re-combine so you can simplify the expression. Practice 1: 8 8 2 4 Practice 2: aa 6 3 Practice 3: 22 2 5 4 Product Property Expand the expressions and then re-combine so you can simplify the expression. Example 3: There are a total of 6 n’s. (m n )( mn ) (m m n n n n)(m n n) m3n 6 2 4 2 There are a total of 3 m’s. Practice 4: ( y z )( y z ) 5 4 2 Product Property Look at the examples and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for multiplying expressions with exponents. Product Property Use the product property to simplify the following. Example 4: 3 8 6 6 6 3 8 6 11 Example 5: 12 4 b b b 12 4 b 16 Product Property Use the product property to simplify the following. Practice 5: 55 5 4 7 Practice 6: x x 3 5 Practice 7: xy x y 5 3 4 To Table of Contents Power of a Power Property Expand the expressions and then re-combine so you can simplify the expression. Example 1: 4 4 4 3 2 3 3 (4 4 4) (4 4 4) 46 There are a total of 6 4’s. Example 2: x x x x x 2 4 2 2 2 2 ( x x ) ( x x ) ( x x) ( x x) x 8 There are a total of 8 x’s. Power of a Power Property Expand the expressions and then re-combine so you can simplify the expression. Practice 1: 12 2 5 Practice 2: w 5 3 Practice 3: 2 3 3 Power of a Power Property Look at the examples and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for raising a power to a power. Power of a Power Property Use the Power of a Power property to simplify the following. Example 3: 5 3 4 5 34 5 12 Example 4: a 4 5 a 45 a 20 Power of a Power Property Use the Power of a Power property to simplify the following. Practice 4: x 3 7 Practice 5: 2 5 3 Practice 6: d 11 4 To Table of Contents Power of a Product Property Expand the expressions and then re-combine so you can simplify the expression. Example 1: x y x y x y x y x y 2 4 2 2 2 2 ( x x y) ( x x y) ( x x y) ( x x y) x y 8 4 There are a total of 8 x’s and 4 y’s. Example 2: 3x y 3x y 3x y 2 5 2 2 5 2 5 3 x x y y y y y 3 x x y y y y y There are a total of 2 3’s, 4 x’s and 10 y’s 3 x y 9x y 2 4 10 4 10 Power of a Product Property Expand the expressions and then re-combine so you can simplify the expression. Practice 1: ab 6 4 Practice 2: 15 19 3 Practice 3: (2 x ) 3 3 Power of a Product Property Look at the examples and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for raising a product to a power. Power of a Product Property Use the Power of a Product property to simplify the following. Example 3: 5x 5 3 5 5 1 ( x ) 515 x35 55 x15 3 5 Example 4: ab c a b c 3 3 3 6 11 3 1 6 11 13 63 113 a b c a b c 3 18 33 Power of a Product Property Use the Power of a Product property to simplify the following. Practice 4: 3x 5 4 Practice 5: a bc 5 6 4 Practice 6: 7a 2 Product, Power of a Power, and Power of a product Properties Use the properties of exponents to simplify the following. Example 5: x x 3 3 1 2 4 (3 x ) x 3 2 3 4 13 23 3 x x 4 3 x x 3 6 4 6 4 27x 27x 10 Product, Power of a Power, and Power of a product Properties Use the properties of exponents to simplify the following. Example 6: 4a b 3a b 4 a b 2 2 2 3 a b 5 2 2 6 1 5 1 2 6 12 52 12 4 a b 3 a b 2 6 4 a b 3 a b 2 10 2 2 6 4 3 a a b b 2 10 2 2 6 10 2 2 6 16 3 a b 48a b 12 8 Product, Power of a Power, and Power of a product Properties Use the properties of exponents to simplify the following. Practice 7: 5x 5x 5 2 Practice 8: 6x y 2x y 2 8 3 3 To Table of Contents Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Example 1: 87 8 8 8 8 8 8 8 88888 5 8 8 8 8 8 8 8 8 Five of the 8’s in the numerator can cancel 88888 with five of the 8’s in the denominator 88 There are two 8’s left 82 64 Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Example 2: x6 x x x x x x x x 2 x x x x x x x Two of the x’s in the numerator can cancel with two of the x’s in the denominator x x xx x x There are four x’s left x4 Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Practice 1: 126 3 12 Practice 2: 7 a 2 a Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Example 3: m 4 n3 m m m m n n n mnn 2 mn One of the m’s in the numerator can mmmmnnn cancel with one of the m’s in the denominator and two of the ns in the mnn numerator can cancel with two of the n’s in the denominator mmmn There are three m’s left and one n left m3n Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Practice 3: a 5b 3 2 ab Quotient Property Look at the examples and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for dividing expressions with exponents. Quotient Property Use the quotient property to simplify the following. Example 4: 12 b 12 4 4 b b 8 b Example 5: 6 8 1 6 6 6 8 8 3 5 6 6 3 3 Quotient Property Use the quotient property to simplify the following. Practice 4: 1 x 7 10 x Practice 5: 9 7 4 7 Practice 6 a3 a6 4 a Practice 7: 11 4 x y 3 2 x y To Table of Contents Power of a Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Example 1: 3 x x x x y y y y xxx y y y 3 x 3 y Power of a Quotient Property Expand the expressions and then re-combine so you can simplify the expression. Practice 1: 4 a 5 Power of a Quotient Property Look at the examples and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for raising a quotient to a power. Power of a Quotient Property Use the power of a quotient property to simplify the following. Example 2: 3 3 6 6 3 x x Example 3: 3 a 1 a 1 3 a 1 a a 3 3 3 3 3 5 5 5 125 125 Power of a Quotient Property Use the power of a quotient property to simplify the following. Practice 2: 5 8 a Practice 3: 6 w z Product, Power of a Power, and Power of a product, Quotient and Power of a quotient Properties Use the properties of exponents to simplify the following. Example 4: 3 3 x 4 4 43 x x x 12 5 5 53 15 3 y y y y Practice 4: 2 a 5 7 b Product, Power of a Power, and Power of a product, Quotient and Power of a quotient Properties Use the properties of exponents to simplify the following. Example 5: 2 x 214 x34 4 4 4 4 2x 3 2x 3 1 3 3 y 3 y 3 y 14 14 3y 4 1 4 1 4 2 x4 12 4 4 3 y 16 x12 4 81 y Product, Power of a Power, and Power of a product, Quotient and Power of a quotient Properties Use the properties of exponents to simplify the following. Example 6: 2 a b 5 23 a 3 b 5 3 3 2a b 5 8 a b3 5 3 3 3b 16 3b 16 3 b 16 27 b 16 3 3 8 a b 3 8 a b 5 1 a 3 b 5 3 3 5 3 27 b 16 16 27 b 3 2 27 3 2 ab 54 Product, Power of a Power, and Power of a product, Quotient and Power of a quotient Properties Use the properties of exponents to simplify the following. Practice 5: 5 2m 5 9 3n Practice 6: 7 x 1 3 8 y 3x Product, Power of a Power, and Power of a product, Quotient and Power of a quotient Properties Use the properties of exponents to simplify the following. Example 7: 3 2 2 2x y x y 3 x y 4 5 2 2 2x y 7 3 2 4 5 31 2 x 7y x y 2 2 2 x y 4 3 4 3 2 x y 3 3 3 2x y 3 2 2 2 2 7 7 2 8 6 3 x y 2 x y 2 6 6 23 x 6 8 y 6 6 8x y 14 12 7 7 2 49 Product, Power of a Power, and Power of a Product, Quotient and Power of a Quotient Properties Use the properties of exponents to simplify the following. Practice 7: 2 4 5a 4b3 4ab 3 ab b To Table of Contents Zero Exponent Property Example 1: Expand the expressions and simplify. x 5 xxxxx xxxxx 1 x 5 xxxxx xxxxx Remember a number divided by itself is 1. Example 2: Use the Quotient rule to simplify the expression. x5 5 x x 55 0 x Zero Exponent Property Practice 1: Expand the expressions and simplify. 4 6 4 6 Practice 2: Use the Quotient rule to simplify the expression. 4 6 4 6 Zero Exponent Property Look at the example and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for raising a term to the zero power. Zero Exponent Property Use the zero property to simplify the following. Example 3: a 1 0 Example 4: 5000 1 0 Example 5: (7 x y ) 1 3 5 0 0 7 5 1 Example 6: x Zero Exponent Property Use the zero property to simplify the following. Practice 3: (6) 0 Practice 4: 1,000,000 0 0 5x y 4 3 Practice 5: 2 10 xy Practice 6: 40ab10 0 To Table of Contents Negative Exponent Property Example 1: Example 2: Expand the expressions and simplify. Use the Quotient rule to simplify the expression. x2 xx 2 x x 5 xxxxx 5 x 25 x3 x x x xxxxx 1 xxx 1 3 x Negative Exponent Property Practice 1: Practice 2: Expand the expressions and simplify. Use the Quotient rule to simplify the expression. 33 3 3 7 3 37 Negative Exponent Property Look at the example and practice problems we have worked. Do you notice a pattern (or rule)? In your own words write a rule for negative exponents. Negative Exponent Property Use the negatvie exponent property to simplify the following. 1 5 Example 3: a 5 a 1 1 Example 4: 5 3 3 5 125 3 6 4 Example 5: 4x y 3 6 x y 4 2 a b Example 6: 2 4 b a Negative Exponent Property Use the negatvie exponent property to simplify the following. 2 Practice 3: 9 6 Practice 4: y 5 Practice 5: 6x y 3 3 Practice 6: 4 x All Properties of Exponents Use the properties of exponents to simplify the following. Example 7: 1 1 2 2 23 2 2 6 6 3 2 64 Example 8: 3 x y 3 3 3 3 3 9 3 3 3 3x y 4 4 x y 12 27 y 12 9 Example 9: x a 2b 4 a5 3 6 a 2( 3)b46 a5b2 a b b2 All Properties of Exponents Use the properties of exponents to simplify the following. Practice 7: 73 5 7 Practice 8: 4a b 2 5 3 Practice 9: 4 x 2 y 4 6 8 xy To Table of Contents

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