1. Lesson 3- using rules of exponents The exponent, tells the number of times that the base is used as a factor 2 3 is defined as 2 times 2 times 2

2. Definition of negative exponents  X -n = 1/x n  2 -3 = 1/2 3

3. simplfy  1/3 -2  3 -3  -3 -2  3 -3  1/5 -2  5 -2  -5 -2  (-5) -2  -(-5) -2

4. Product rule for exponents  x m x n = x m+n

5. Power rule for exponents  (x m ) n = x mn

6. Scientific notation  Multiplying by a positive power of 10, moves the decimal point to the right.  Multiplying by a negative power of 10, moves the decimal point to the left

7. Simplifying expressions in scientific notation  (4.2 x 10- 7 )(.0028)  2400(1.6 x 10 -10 )  (.0003 x 10 -6 )(4000)  (.006 x 10 15 )(2000 x 10 4 )

8. Lesson 6 finding percent of change  Any fraction or decimal can be written as a percent.  To write a decimal as a percent, multiply by 100(move decimal point 2 places to the left)  To write a fraction as a percent, divide the numerator by the denominator, then multiply by 100

9. examples  Change.12 to a percent  Change 8 to a percent  Change 4/5 to a percent  Change 22/8 to a percent  Change.035 to a percent

10. Percent of change  Percent of change is the increase or decrease given as a percent of the original amount  When the new amount is greater than the original amount, the change is a percent increase  When the new amount is less then the original amount, the change is a percent decrease

11. Percent of change  Percent of change= amount of increase or decrease  original amount

12. practice  Calculate the percent of change and tell whether it is an increase or decrease.  From 120 to 168  From 6 to 5.1  From 18 to 72  From 240 to 60

13. Determining new amount  What is the new amount when 58 is decreased by 70%?  1. find amount of decrease  70% of 58=.70x58 = 40.6  2. subtract amount of decrease from original amount  58-40.6= 17.4  OR  1. subtract 70% from 100% = 30%  2. find 30% of 58 = 17.4

14. What is the new amount when 125 is decreased by 15%  1..15 x 125=18.75  2. 125-18.75= 106.25  Or  1. 100%- 15%= 85%  2. 85% x 125 = 106.25

15. Find new amount when 620 is increased by 350%.  1. find 350% of 620 = 3.5 x 620 =2170  2.add 2170 to 620= 2790  Or  1. add 100% to 350%= 450%  2. find 450% of 620= 4.5 x 620= 2790

16. discount  When an item in a store is on sale, the new price reflects a discount.  The amount of discount is the difference between the old and new price and the percent of discount is a percent of discount

17.  When the price of an item increases, the increase is a markup, and the percent of change is a percent increase.  A markup can refer to an increase in the retail price of an item or it can refer to the amount by which the wholesale cost of the item is increased.  Marked up price=original price +markup  =(wholesale price) + markup  Sale price = original price - discount

18. Find sale price  A digital camera costs $128. It is being offered at a 25% discount. Find the sale price.  Sale price = original price - discount  S = 128 - 25% x 128  S = 128 -32= $96  Or  100% -25% = 755  75% of 128 = 96

19. Finding marked up price  A grocer buys watermelon from a farmer for $1.34 each and sells them at a 250% markup. What is the cost of the watermelon at the grocer's store.  Marked up price= wholesale price+ markup  = 1.34+ 250% of 1.34  =1.34 + 3.35  = 4.69

20. Check for understanding  Explain how to find the new amount when a number is increased by a percent.  Explain the difference between a discount and a markup.  A student states that a negative exponent means the exponential must be in the denominator. Is this correct? Explain.