Properties of Exponents Multiplication Property When you multiply terms with the same base you add the exponents xm * xn = xm+n So as an example… x2 * x4 = x2+4 = x6

Properties of Exponents Division Property When you divide terms with the same base you subtract the exponents (top – bottom) xm / xn = xm-n So as an example… x5 * x2 = x5-2 = x3

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 (xmyn)k = xm*kyk*n So as an example… (x5y2)4 = x5(4)y2(4) = x20y8

Properties of Exponents Zero Exponents Anything except zero raised to the zero power is equal to 1 x0 = 1 Why? x x1 = = x1-1 x x1 But… x We know that So… = 1 x x0 = 1

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 1 1 xn x-n = = xn xn = x-n 1

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

Scientific Notation - Expansion Scientific Notation uses a number between 1 and 10 (but not equal to 10) that is raised to a power of 10 2.834 x 104 = 28340 (move the decimal 4 places to the right) 2.834 x 10-2 = .02834 (move the decimal 2 places to the left)

Scientific Notation - Contraction 42502 = 4.2502 x 104 (exponent means you moved the decimal 4 places to the left) .00002469 = 2.469 x 10-5 (exponent means you moved the decimal 5 places to the right)

Practice 2x2 * 4x3 = 8x5 6x6y7 3x3 = 3x3y-2 = 2x3y9 y2

Practice (2a3b2)3 8a9b6 23a9b6 = = 4a3b9 4a3b9 4a3b9 = 2a6b-3 2a6 = b3

Homework Answers 22) 32 * 36 = 38 27) (3 * 7)2 = 32 * 72 Keep the base the same and add the exponents 27) (3 * 7)2 = 32 * 72 Distribute the exponent to ALL exponents in the parenthesis 40) 2x3 * (3x)2 = 2x3 * 32x2 = 2x3 * 9x2 = 18x5

Homework Answers 47) (6a4)2 * (1/4a2)2 = 62a8 *(1/4)2a4 = 36a8 *(1/16)a4 = (36/16)a12 14) 4-2 = 4-2/1 = 1/42 24) 8-7 * 87 = (1/87) * 87 = 87/87 = 1

Homework Answers 34) x4y-7 = x4(1/y7) = x4 /y7 39) (-4x)-3 = (-4)-3x-3 = 1/((-4)3x3) = 1/(-64x3) 31) (3)4 81 = x4 (x)4

Homework Answers 43) 4x4y3 5xy2 * 2y 2xy 20x5y5 = 5x4y3 4xy2

Homework pg 473 – #16, 20, 27, 35 pg 453 - #43, 52 pg 459 #37, 43, 44 pg 466 #42, 44, 47, 48