Simplifying Algebraic expressions Section 1.4 Simplifying Algebraic expressions

Evaluating an expression You will be given a value for one or all variables, then be asked to evaluate it. Ex Given x = 3 y = 4, evaluate 4x – 2y Answer: 4(3) – 2(4) = 12 – 8 = 4

Simplifying experssions You will be given an expression in expanded form Combine all like terms Ex x2 – 3x + 2y +2x2 + 4x – 3y = = 3x2 + x + 6y

More Complex example x(3x – 2y) – 3xy + 2x + 4x2 Distribute first = 3x2 – 2xy – 3xy + 2x + 4x2 Combine like terms 7x2 – 5xy +2x

Homework Pg30 (1-7, 15-18, 27, 36, 38, 50, 51)

Properties of Exponents Section 1.5 Properties of Exponents

This means that x is multiplied by itself “a” times Exponents Example xa x is the base a is the exponent This means that x is multiplied by itself “a” times Ex: x4 means (x)(x)(x)(x) Show them how to do exponents on the calculator using smart view

Find the Following by hand 62 33 24 102 1. 36 2. 27 3. 16 4. 100

Negative signs in the base number Find the following by using your calculator (-5)3 and -53 (-5)(-5)(-5) -[(5)(5)(5)] Do they work out to be the same number? Yes both are -125 Will this always be the case?

Try these in your calculator (-4)3 and -43 (-4)(-4)(-4) -[(4)(4)(4)] Do they work out to be the same number? No both are 64, but one is – and one is + Brackets make a difference

Negative Exponents x-n = 1/(xn) Also 1/(x-n) = xn

Try these examples [(4)(3)]-2 (12)-2 1/(122) 1/144 (3-2)/(23) 1/[(32)(23)] 1/[(8)(9)] 1/72 1/(10x)-3 (1)(10x)3 (103)(x3)

(xm)(xn)= xm+n where m & n are positive integers Product of Powers (xm)(xn)= xm+n where m & n are positive integers in order for this to work the base of both numbers must be the same The exponents can be different

(22)(23) = 22+3 = 25 = 32 (-12mn7)(6m3n2) = (-12)(6)(m)(m3)(n7)(n2) Examples (22)(23) = 22+3 = 25 = 32

(7)(4)(10)(c3)(c2)(c4)(d2)(d)(d6) Try This (7c3d2)(4c2d)(10c4d6) (7)(4)(10)(c3)(c2)(c4)(d2)(d)(d6) (280)(c3 +2+4)(d2+1+6) 280c9d9

(xm)n = xmn where m & n are positive integers (x4)7 = x(4)(7) = x28 Power of a Power (xm)n = xmn where m & n are positive integers Example (x4)7 = x(4)(7) = x28

(-3x)4 (3)(-3x2)4 =(-3)4(x)4 =(3)(-3)4(x2)4 81x4 =(3)(81)(x(2)(4)) Try these (-3x)4 =(-3)4(x)4 81x4 (3)(-3x2)4 =(3)(-3)4(x2)4 =(3)(81)(x(2)(4)) =243x8

(2x3)4 = (24)(x3)4 =16x12 Power of a Product (xy)n = xnyn where n is a positive integer Example (2x3)4 = (24)(x3)4 =16x12

Try this 3(-3x2)4 3(-3)4(x2)4 3(81)(x(2)(4)) 243x8

[(x2)/(y6)]4 (x2)4/(y6)4 (x8)/(y24) Power of a quotient (x/y)n = (xn)/(yn) where n is a positive integer Example [(x2)/(y6)]4 (x2)4/(y6)4 (x8)/(y24)

[(2ab2)/(3c3d)]5 (2ab2)5/(3c3d)5 (25a5b(2)(5))/(35c(3)(5)d5) Try this [(2ab2)/(3c3d)]5 (2ab2)5/(3c3d)5 (25a5b(2)(5))/(35c(3)(5)d5) (32a5b10)/(243c15d5)

Quotients of Powers (xm)/(xn) = xm – n If m-n is negative then you must continue the simplification Example (14x7)/(2x5) 7x7 – 5 7x2

Try this (-2y4)/(8y10) = -(1/4)(y4 – 10) = -(1/4)(y-6) = -(1/4y6)

Zero and Negative Exponents Use the properties of exponents to find the following. (23)/(23) By using properties of exponents we would subtract in this case so: 23-3= 20 Also could be done this way: = 8/8 = 1

Definition For every number x, (not equal to 0) The following holds true x0 = 1

____ x 10 a (# between 1 and 10) (can be positive or negative) Example 2.3 x 106 = 2300. 2.3 x 10-6 = .0000023 If there is a positive exponent the decimal moves right If there is a negative exponent the decimal moves left

Express the following in scientific notation 645000 Would it be… Going backwards Express the following in scientific notation 645000 Would it be… 64.5 x 104 Or 6.45 x 105 Make them aware the number must be between 1 and 10 so the second one is the correct answer

5.1 x 106 3.4 x 103 5.1 x 103 3.4 1.5 x 103 5.1 x 103 3.4 x 106 5.1 x 10-3 3.4 1.5 x 10-3 Have them try 1 then go over it then try 2 and review it

Homework Pg38 (1-13 odd, 19,24,30,31,39,58,83-86)