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Properties of Exponents Multiplication Property When you multiply terms with the same base you add the exponents x m * x n = x m+n So as an example… x 2 * x 4 = x 2+4 = x 6

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Properties of Exponents Division Property When you divide terms with the same base you subtract the exponents (top – bottom) x m / x n = x m-n So as an example… x 5 * x 2 = x 5-2 = x 3

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Properties of Exponents Power raised to a Power When you have a power outside of parenthesis you multiply ALL exponents inside by the exponent outside (x m y n ) k = x m*k y k*n So as an example… (x 5 y 2 ) 4 = x 5(4) y 2(4) = x 20 y 8

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Properties of Exponents Zero Exponents Anything except zero raised to the zero power is equal to 1 x 0 = 1 But… We know that Why? x x x1x1 x1x1 ==x 1-1 =1 x x So… x 0 = 1

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Properties of Exponents Negative Exponents Any time you have a negative exponent you move the term with the negative exponent to the opposite part of the fraction and make it positive x -n = 1 xnxn 1 = x n 1 = xnxn

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Homework pg 453 #22, 27, 40, 47 pg 459 #14, 24, 34, 39 Pg 466 #31, 43, 45, 46 pg 473 – #16, 20, 27, 35

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Scientific Notation - Expansion Scientific Notation uses a number between 1 and 10 (but not equal to 10) that is raised to a power of x 10 4 = (move the decimal 4 places to the right) x = (move the decimal 2 places to the left)

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Scientific Notation - Contraction = x 10 4 (exponent means you moved the decimal 4 places to the left) = x (exponent means you moved the decimal 5 places to the right)

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Practice 2x 2 * 4x 3 = 8x 5 6x 6 y 7 2x 3 y 9 = 3x 3 y -2 3x 3 y 2 =

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Practice (2a 3 b 2 ) 3 4a 3 b 9 23a9b623a9b6 = 8a 9 b 6 4a 3 b 9 = =2a 6 b -3 = 2a 6 b3b3

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Homework Answers 22) 3 2 * 3 6 Keep the base the same and add the exponents ) (3 * 7) 2 = 40) 2x 3 * (3x) 2 =3 2 * 7 2 Distribute the exponent to ALL exponents in the parenthesis = 2x 3 * 3 2 x 2 = 2x 3 * 9x 2 = 18x 5

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Homework Answers 47) (6a 4 ) 2 * ( 1 / 4 a 2 ) 2 = 6 2 a 8 *(1/4) 2 a 4 = 36a 8 *(1/16)a 4 = (36/16)a 12 14) 4 -2 = 4 -2 /1= 1/4 2 24) 8 -7 * 8 7 = (1/8 7 ) * 8 7 = 8 7 /8 7 = 1

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Homework Answers 34) x 4 y -7 = x 4 (1/y 7 ) 39) (-4x) -3 31) (3) 4 = x 4 /y 7 = (-4) -3 x -3 = 1/((-4) 3 x 3 ) = 1/(-64x 3 ) (x) 4 = 81 x 4

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Homework Answers 43) 4x 4 y 3 * 2xy 5xy 2 2y 20x 5 y 5 4xy 2 = 5x 4 y 3

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Homework pg 473 – #16, 20, 27, 35 pg #43, 52 pg 459 #37, 43, 44 pg 466 #42, 44, 47, 48

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