1. Simplifying Algebraic expressions
Section 1.4
Simplifying Algebraic expressions

2. 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

3. 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

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

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

6. Properties of Exponents
Section 1.5
Properties of Exponents

7. 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

8. Find the Following by hand 62 33 24 102
1. 36

9. Negative signs in the base number
Find the following by using your calculator
(-5) and
(-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?

10. Try these in your calculator
(-4) and
(-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

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

12. 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)

13. (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

14. (22)(23) = 22+3 = 25 = 32 (-12mn7)(6m3n2) = (-12)(6)(m)(m3)(n7)(n2)
Examples
(22)(23)
= 22+3
= 25
= 32

15. (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

16. (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

17. (-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

18. (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

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

20. [(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)

21. [(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)

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

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

24. 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

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

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

27. 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

28. 5.1 x 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

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